why x=y2-5y is not a function but y x2-5 is
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punzvrf1
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So the question is asking why x=y2-5y is not a function but x=y2-5y is not. The question also says to substitute -6 with x to solve for 1. (the 2 is an exponent just so you know). I solved y=66 in the first one, but got -1 for the second...??
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1. Market research has determined the following changes in market shares based on the different combinations of music choi ...
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Follow instructions attached, original work.This task assesses the following learning outcomes:
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Working Capital Requirement and Ratio Over Sales Discussion
Follow instructions attached, original work.This task assesses the following learning outcomes:
Critically understand and apply tools for financial statements analysis
Properly elaborate a Free Cash Flow calculation
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Running Inferential Statistics—t Tests
A t test examines if two means (averages) are reliably different from each other; that is, whether any significant differe ...
Running Inferential Statistics—t Tests
A t test examines if two means (averages) are reliably different from each other; that is, whether any significant differences exist between the means of samples from different populations. For example, to what extent is the output of a local office which applied an IT solution different than the output of other local offices which did not apply the IT solution? Also, if you wanted to test whether the average IQ score of a group of students differs from 100, you may use a t test. A t test does more than just compare means; as an inferential statistic, t tests allow researchers to make inferences about the populations beyond their sample data.For this Assignment, you will use the IT Security database and conduct two t tests: (a) one-sample t test and (b) paired-samples t test and prepare an APA results write-up for each test.To prepare for this Assignment:Review the media programs:Introduction to Hypothesis TestingThe t StatisticThe t Test for Related SamplesEstimationReview Lesson 22, "One-Sample t Test.” Then conduct a one-sample t test using the IT Security Dataset from this week’s Learning Resources.Pay particular attention to the sections titled “Writing an APA Results Section” (on pages 119-120) and “An APA Results Section” (on page 167) in the Green and Salkind text.Review Lesson 23, “Paired-Samples t Test.” Then conduct a paired-samples t test using the IT Security Dataset.Pay particular attention to the section titled “An APA Results Section” (on page 122) in the Green and Salkind text.Review the Assignment Exemplar provided in this week’s Learning Resources.Submit a 5- to 6-page paper using the Assignment Exemplar.Your paper must include the following elements:An APA Results section for each t test. (See examples of APA Results sections in Lesson 22 (one-sample t test) and Lesson 23 (paired-samples t test) of the Green and Salkind text.)The critical elements of your SPSS output, including:A properly formatted research questionA properly formatted H10 (null) and H1a (alternate) hypothesisA descriptive statistics narrative and properly formatted descriptive statistics table (see page 148 of the Green and Salkind text)A properly formatted histogram for the one-sample t test (see page 149 of the Green and Salkind text)A properly formatted box plot for the paired-samples t test (see page 154 of the Green and Salkind text)A properly formatted inferential APA Results Section (see page 149 of the Green and Salkind text) for each testAn appendix including the SPSS output generated for descriptive and inferential statistics (see SPSS output on page 148 of the Green and Salkind text)
Linear Regression Project
In this project you will chose a data set that interests you and investigate a possible association between two variables ...
Linear Regression Project
In this project you will chose a data set that interests you and investigate a possible association between two variables within that data set. This project will give you an opportunity to use StatCrunch to apply the skills and techniques you have learned in this class and to produce a professional report. To produce a successful project you must:Read and follow the instructions carefully.Give yourself sufficient time to work on the project.Write clearly, using appropriate statistical terminology and correct mathematical notation. College-level writing is expected, as is the use of proper grammar.Use StatCrunch to complete all calculations and graphs.Create original work. The following link describes, in detail, plagiarism, fair use and HCC’s academic policy: Fair Use and Academic Honesty (Links to an external site.) Furthermore, this means that students who are repeating the course are expected to create an entirely new project using two new variables of interest.Submit a professional report that is typed and formatted and organized wellSubmit your project via Canvas as a PDF or Word file.PROJECT INSTRUCTIONSFor this project you are going to choose one data set from the list below that you find interesting and investigate an association between two variables within that data set. You will then examine the data and write a two page report. In your report you should:Introduce the data set and explain why you chose it.Describe the variables you chose and thoroughly explain what you are investigating. Be sure to define which variable is the explanatory variable and which is the response variable.Using StatCrunch, create an appropriate graph for the association you are investigating and calculate the correlation coefficient and the linear model. Be sure your graph is appropriately labeled and that it includes a title and then copy it into your paper.Report the correlation coefficient.Describe the association you are investigating using correct statistical terminology. Reference your graph and the correlation coefficient, and be sure to note any possible outliers.Report the linear model using correct notation.Interpret the slope and vertical intercept of your model, and discuss the appropriateness of your model.Summarize your findings and draw a conclusion.DATA SETSBelow is a list of data sets - choose one for your project. The links will not work directly, so please follow these directions: In Canvas, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website --> Open StatCrunch (yellow button at top of page, it will auto login)Then copy/paste a URL below into either the current tab or a new tabTo save your data and work, go to the Data tab and choose SaveTo Re-open your saved file, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website -->MyStatCrunch (on the right side)-->My DataMarriage vs. the Economy: https://www.statcrunch.com/app/index.php?dataid=28... This data set compares the number of marriages in the last 30 years to several factors of the economy. COMPLETION CHECKLISTUse the following checklist when proofreading your project.For each aspect below, an excellent report will: IntroductionGive the name of the data set chosen as well as some details describing the data set. (This may require following links or referencing the text)Include a clear justification for why the data set was chosen.Involve two quantitative variables.Clearly and thoroughly describe the variables chosen. (This may require following links or referencing the text)Clearly and correctly assign explanatory and response variables.Thoroughly explain the association being investigated and give a logical justification for why the author believes the association exists.GraphInclude an appropriate scatterplot generated using StatCrunch.Accurately assign and clearly label the axes for the scatterplot.Include an appropriate title for the scatterplot. Include the appropriate correlation coefficient for the association generated using StatCrunch.Include an accurate and thorough description of the association with reference to the graph, correlation coefficient and any outliers. Linear Association ModelInclude an appropriate linear regression model generated using StatCrunch and written using correct notation and typesetting.Give an accurate and detailed interpretation of the slope of the linear regression model.Give an accurate and detailed interpretation of the y-intercept of the linear regression model.Thoroughly discuss the appropriateness of the linear regression model with reference to other aspects of the report.ConclusionIncludes a summary of the findings and a clear conclusion regarding the association.Appear highly professional, be easy to read and comprehend, and use correct statistical vocabulary.
Montgomery College Critical Thinking and Express the Confidence Interval Worksheet
EXP 10 Practice Express the confidence interval 61 % ± 5.9 % in interval form. Express the answer in decimal format ( ...
Montgomery College Critical Thinking and Express the Confidence Interval Worksheet
EXP 10 Practice Express the confidence interval 61 % ± 5.9 % in interval form. Express the answer in decimal format (do not enter as percents). We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 153 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county. Give your answers as decimals, to three places. < p < Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 105 with 33.3% successes at a confidence level of 99.9%. M.E. = % Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 7 2 16 25 Female 5 3 6 14 Total 12 5 22 39 Let π represent the percentage of all female students who would receive a grade of A on this test. Use a 90% confidence interval to estimate p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents). < p < A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people. Critical thinking 10 Application 10 Find an example of a confidence interval for a proportion in the media or scholarly literature (do not use a statistics textbook or website/article that is teaching or demonstrating statistics to find the example). At the very least it must include either the lower and upper bounds or a point estimate with a margin of error. Make sure you have a Proportion confidence interval and NOT a CI for the mean, odds ratio, hazard ratio, or relative risk as these will result in having to REDO the assignment (a) Include a digital photo/screenshot of the original appearance of the confidence interval and a link to the website (or citation) where it can be found. (b) Write the confidence interval in the form (lower bound, upper bound). If there are multiple confidence intervals, just pick one. (c) State the population parameter this confidence interval is trying to estimate. (d) State the confidence level and sample size. If no confidence level is given assume it is 95%95%. (e) Use the point estimate, confidence level, and sample size to calculate the confidence interval and compare your calculated values with those published in the article. (f) State what the sample and population were for the study. Infer this information if it is not provided (g) Comment on the source for the data, the publisher of the CI, and their purpose for doing so. Put the above in a document and upload your complete file below. Question 1Choose FileNo file chosen Exp 11 Practice Less than 35% of workers indicate that they are satisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0:pH0:p H1:pH1:p Use the following codes to enter the following symbols: ≥≥ enter >= ≤≤ enter <= ≠≠ enter != A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one-way commute time of 38 minutes with a standard deviation of 8 minutes. Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes? H0: μ = 30; HA: μ ≠ 30 HA: μ = 30; H0: x ≠ 30 H0: x = 38; HA: μ = 30 H0: μ = 30; HA: μ > 30 H0: μ = 30; HA: x = 38 A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context? The local government decides that the average commute time is 30 minutes. The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes. Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: the food is safe Ha: the food is not safe The following is an example of what type of error? The sample suggests that the food is safe, but it actually is not safe. type I type II not an error If your null and alternative hypothesis are: H0: p=0.3 H1: p>0.3 Then the test is: left tailed right tailed two tailed If your claim is in the null hypothesis and you fail to reject the null hypothesis, then your conclusion would be: The sample data support the original claim There is sufficient evidence to warrant rejection of the original claim There is not sufficient sample evidence to support the original claim There is not sufficient evidence to warrant rejection of the original claim A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position. Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test. The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position. Because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test. Critical Thinking Questions How do you decide whether to reject or fail to reject the null hypothesis? [1 sentence] How do you tell whether the test is left, right, or two tailed? [3 bullets] Why can we never accept the null hypothesis? [2 sentences] Why does decreasing the probability of making a type one error increase the probability of making a type two error? [2 sentences] How does a researcher decide the level of significance for a hypothesis test? [3 sentences]
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2 pages
Mat220 Statistics Graphical Displays Of Data
Generally, graphs are extremely powerful mechanisms for viewing large quantities of complex data; they assists turn the re ...
Mat220 Statistics Graphical Displays Of Data
Generally, graphs are extremely powerful mechanisms for viewing large quantities of complex data; they assists turn the realms of data available into ...
4 pages
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1. Market research has determined the following changes in market shares based on the different combinations of music choi ...
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Working Capital Requirement and Ratio Over Sales Discussion
Follow instructions attached, original work.This task assesses the following learning outcomes:
Critically ...
Working Capital Requirement and Ratio Over Sales Discussion
Follow instructions attached, original work.This task assesses the following learning outcomes:
Critically understand and apply tools for financial statements analysis
Properly elaborate a Free Cash Flow calculation
Utilize financial indicators to interpret a company’s profitability and liquidity
Running Inferential Statistics—t Tests
A t test examines if two means (averages) are reliably different from each other; that is, whether any significant differe ...
Running Inferential Statistics—t Tests
A t test examines if two means (averages) are reliably different from each other; that is, whether any significant differences exist between the means of samples from different populations. For example, to what extent is the output of a local office which applied an IT solution different than the output of other local offices which did not apply the IT solution? Also, if you wanted to test whether the average IQ score of a group of students differs from 100, you may use a t test. A t test does more than just compare means; as an inferential statistic, t tests allow researchers to make inferences about the populations beyond their sample data.For this Assignment, you will use the IT Security database and conduct two t tests: (a) one-sample t test and (b) paired-samples t test and prepare an APA results write-up for each test.To prepare for this Assignment:Review the media programs:Introduction to Hypothesis TestingThe t StatisticThe t Test for Related SamplesEstimationReview Lesson 22, "One-Sample t Test.” Then conduct a one-sample t test using the IT Security Dataset from this week’s Learning Resources.Pay particular attention to the sections titled “Writing an APA Results Section” (on pages 119-120) and “An APA Results Section” (on page 167) in the Green and Salkind text.Review Lesson 23, “Paired-Samples t Test.” Then conduct a paired-samples t test using the IT Security Dataset.Pay particular attention to the section titled “An APA Results Section” (on page 122) in the Green and Salkind text.Review the Assignment Exemplar provided in this week’s Learning Resources.Submit a 5- to 6-page paper using the Assignment Exemplar.Your paper must include the following elements:An APA Results section for each t test. (See examples of APA Results sections in Lesson 22 (one-sample t test) and Lesson 23 (paired-samples t test) of the Green and Salkind text.)The critical elements of your SPSS output, including:A properly formatted research questionA properly formatted H10 (null) and H1a (alternate) hypothesisA descriptive statistics narrative and properly formatted descriptive statistics table (see page 148 of the Green and Salkind text)A properly formatted histogram for the one-sample t test (see page 149 of the Green and Salkind text)A properly formatted box plot for the paired-samples t test (see page 154 of the Green and Salkind text)A properly formatted inferential APA Results Section (see page 149 of the Green and Salkind text) for each testAn appendix including the SPSS output generated for descriptive and inferential statistics (see SPSS output on page 148 of the Green and Salkind text)
Linear Regression Project
In this project you will chose a data set that interests you and investigate a possible association between two variables ...
Linear Regression Project
In this project you will chose a data set that interests you and investigate a possible association between two variables within that data set. This project will give you an opportunity to use StatCrunch to apply the skills and techniques you have learned in this class and to produce a professional report. To produce a successful project you must:Read and follow the instructions carefully.Give yourself sufficient time to work on the project.Write clearly, using appropriate statistical terminology and correct mathematical notation. College-level writing is expected, as is the use of proper grammar.Use StatCrunch to complete all calculations and graphs.Create original work. The following link describes, in detail, plagiarism, fair use and HCC’s academic policy: Fair Use and Academic Honesty (Links to an external site.) Furthermore, this means that students who are repeating the course are expected to create an entirely new project using two new variables of interest.Submit a professional report that is typed and formatted and organized wellSubmit your project via Canvas as a PDF or Word file.PROJECT INSTRUCTIONSFor this project you are going to choose one data set from the list below that you find interesting and investigate an association between two variables within that data set. You will then examine the data and write a two page report. In your report you should:Introduce the data set and explain why you chose it.Describe the variables you chose and thoroughly explain what you are investigating. Be sure to define which variable is the explanatory variable and which is the response variable.Using StatCrunch, create an appropriate graph for the association you are investigating and calculate the correlation coefficient and the linear model. Be sure your graph is appropriately labeled and that it includes a title and then copy it into your paper.Report the correlation coefficient.Describe the association you are investigating using correct statistical terminology. Reference your graph and the correlation coefficient, and be sure to note any possible outliers.Report the linear model using correct notation.Interpret the slope and vertical intercept of your model, and discuss the appropriateness of your model.Summarize your findings and draw a conclusion.DATA SETSBelow is a list of data sets - choose one for your project. The links will not work directly, so please follow these directions: In Canvas, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website --> Open StatCrunch (yellow button at top of page, it will auto login)Then copy/paste a URL below into either the current tab or a new tabTo save your data and work, go to the Data tab and choose SaveTo Re-open your saved file, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website -->MyStatCrunch (on the right side)-->My DataMarriage vs. the Economy: https://www.statcrunch.com/app/index.php?dataid=28... This data set compares the number of marriages in the last 30 years to several factors of the economy. COMPLETION CHECKLISTUse the following checklist when proofreading your project.For each aspect below, an excellent report will: IntroductionGive the name of the data set chosen as well as some details describing the data set. (This may require following links or referencing the text)Include a clear justification for why the data set was chosen.Involve two quantitative variables.Clearly and thoroughly describe the variables chosen. (This may require following links or referencing the text)Clearly and correctly assign explanatory and response variables.Thoroughly explain the association being investigated and give a logical justification for why the author believes the association exists.GraphInclude an appropriate scatterplot generated using StatCrunch.Accurately assign and clearly label the axes for the scatterplot.Include an appropriate title for the scatterplot. Include the appropriate correlation coefficient for the association generated using StatCrunch.Include an accurate and thorough description of the association with reference to the graph, correlation coefficient and any outliers. Linear Association ModelInclude an appropriate linear regression model generated using StatCrunch and written using correct notation and typesetting.Give an accurate and detailed interpretation of the slope of the linear regression model.Give an accurate and detailed interpretation of the y-intercept of the linear regression model.Thoroughly discuss the appropriateness of the linear regression model with reference to other aspects of the report.ConclusionIncludes a summary of the findings and a clear conclusion regarding the association.Appear highly professional, be easy to read and comprehend, and use correct statistical vocabulary.
Montgomery College Critical Thinking and Express the Confidence Interval Worksheet
EXP 10 Practice Express the confidence interval 61 % ± 5.9 % in interval form. Express the answer in decimal format ( ...
Montgomery College Critical Thinking and Express the Confidence Interval Worksheet
EXP 10 Practice Express the confidence interval 61 % ± 5.9 % in interval form. Express the answer in decimal format (do not enter as percents). We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 153 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county. Give your answers as decimals, to three places. < p < Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 105 with 33.3% successes at a confidence level of 99.9%. M.E. = % Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 7 2 16 25 Female 5 3 6 14 Total 12 5 22 39 Let π represent the percentage of all female students who would receive a grade of A on this test. Use a 90% confidence interval to estimate p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents). < p < A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people. Critical thinking 10 Application 10 Find an example of a confidence interval for a proportion in the media or scholarly literature (do not use a statistics textbook or website/article that is teaching or demonstrating statistics to find the example). At the very least it must include either the lower and upper bounds or a point estimate with a margin of error. Make sure you have a Proportion confidence interval and NOT a CI for the mean, odds ratio, hazard ratio, or relative risk as these will result in having to REDO the assignment (a) Include a digital photo/screenshot of the original appearance of the confidence interval and a link to the website (or citation) where it can be found. (b) Write the confidence interval in the form (lower bound, upper bound). If there are multiple confidence intervals, just pick one. (c) State the population parameter this confidence interval is trying to estimate. (d) State the confidence level and sample size. If no confidence level is given assume it is 95%95%. (e) Use the point estimate, confidence level, and sample size to calculate the confidence interval and compare your calculated values with those published in the article. (f) State what the sample and population were for the study. Infer this information if it is not provided (g) Comment on the source for the data, the publisher of the CI, and their purpose for doing so. Put the above in a document and upload your complete file below. Question 1Choose FileNo file chosen Exp 11 Practice Less than 35% of workers indicate that they are satisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0:pH0:p H1:pH1:p Use the following codes to enter the following symbols: ≥≥ enter >= ≤≤ enter <= ≠≠ enter != A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one-way commute time of 38 minutes with a standard deviation of 8 minutes. Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 30 minutes? H0: μ = 30; HA: μ ≠ 30 HA: μ = 30; H0: x ≠ 30 H0: x = 38; HA: μ = 30 H0: μ = 30; HA: μ > 30 H0: μ = 30; HA: x = 38 A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context? The local government decides that the average commute time is 30 minutes. The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes. Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: the food is safe Ha: the food is not safe The following is an example of what type of error? The sample suggests that the food is safe, but it actually is not safe. type I type II not an error If your null and alternative hypothesis are: H0: p=0.3 H1: p>0.3 Then the test is: left tailed right tailed two tailed If your claim is in the null hypothesis and you fail to reject the null hypothesis, then your conclusion would be: The sample data support the original claim There is sufficient evidence to warrant rejection of the original claim There is not sufficient sample evidence to support the original claim There is not sufficient evidence to warrant rejection of the original claim A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position. Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test. The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position. Because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test. Critical Thinking Questions How do you decide whether to reject or fail to reject the null hypothesis? [1 sentence] How do you tell whether the test is left, right, or two tailed? [3 bullets] Why can we never accept the null hypothesis? [2 sentences] Why does decreasing the probability of making a type one error increase the probability of making a type two error? [2 sentences] How does a researcher decide the level of significance for a hypothesis test? [3 sentences]
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