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1 AB is tangent to C because AB^2 + BC^2=AC^2
12*12+9*9=15*15
144+81=225
225=225.....ANGLE ABC=90, degrees
2 AB is not tangent to C this is not a right angled triangle.
Length of line AB (12) cannot be longer than line CB (9)
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module 5 and exam
Problem Set 5.1Problem Set 5.11. Describe, in your own words the sampling distribution of x̄.- Click here to enter answer ...
module 5 and exam
Problem Set 5.1Problem Set 5.11. Describe, in your own words the sampling distribution of x̄.- Click here to enter answer - 2. For the sampling distribution of x̄, is it necessary that the samples used in the distribution be all of the same size?- Click here to enter answer - 3. What is E(x̄)? What is E(x̄) equal to?- Click here to enter answer - 4. Suppose you take a random sample and find the sample mean, x̄. Based on the previous problem, can you say that x̄ is equal to the mean of the entire population µ?- Click here to enter answer - Problem Set 5.2Problem Set 5.21. Suppose that you are attempting to estimate the weight of 600 parts. In order to use the infinite standard deviation formula, what sample size, n, should you use?- Click here to enter answer - 2. A nursing home has 2000 patients. You sample 170 patients. Can you use the infinite standard deviation formula?- Click here to enter answer - 3. Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - 4. Suppose that you take a sample of size 20 from a population that is not normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - 5. Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - Problem Set 5.3Problem Set 5.31. Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. Let's assume that there are 4,300 sales people and the population mean for the sales force is $52,400 in commissions and has a population standard deviation of $3,500. What is the probability that a simple random sample of 50 members of the sales force will have commissions within $400 of the population mean?- Click here to enter answer - 2. Suppose that in a certain large city, the mean 100 meter dash time for male high school seniors was reported to be 13.3 seconds with a standard deviation of 1.9 seconds. We may assume that the population is normally distributed.a) What is the probability that 20 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?- Click here to enter answer - b) What is the probability that 40 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?- Click here to enter answer - c) What is the probability that 35 male high school seniors selected at random will have a mean 100 meter dash time between 13 seconds and 14 seconds?- Click here to enter answer - 3. Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution.a) If you choose 25 potatoes at random, what is the probability that the mean of this sample of 25 potatoes is between 7 and 8 ounces?- Click here to enter answer -b) If you choose 45 potatoes at random, what is the probability that the mean of this sample of 45 potatoes is less than 7 ounces?- Click here to enter answer -c) If you choose 40 potatoes at random, what is the probability that the mean of this sample of 40 potatoes is more than 7.5 ounces?- Click here to enter answer -Problem Set 5.4Problem Set 5.41. According to the American Diabetes Association (2013), 8.3 % of the U.S. population have diabetes.a) Suppose that you take a random of 80 Americans, what is the probability that 7 % or less of these 80 people have diabetes?- Click here to enter answer - b) Suppose that you take a random of 120 Americans, what is the probability that 8 % or more of these 120 people have diabetes?- Click here to enter answer -
2 questions on worksheet.
07.04 Mathematical InductionAssignment Name: ___________________________________Print this page or copy and paste this ass ...
2 questions on worksheet.
07.04 Mathematical InductionAssignment Name: ___________________________________Print this page or copy and paste this assignment in to a word document.After filling in the requested information below, you may either scan your handwritten work or take a clear digital picture. You will need to save the scanned copy or digital picture of your work in order to submit as a file attachment.Note: When saving files, please remember that you should not use a period or a space in your file name. It is recommended that you use the underscore when saving your documents: 1_01, 1_02pg1, 1_02og2, etc. Contact your instructor if you have questions about saving files.Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.(4 points each.)4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 12 + 42 + 72 + ... + (3n - 2)2 = For the given statement Pn, write the statements P1, Pk, and Pk+1.(2 points)2 + 4 + 6 + . . . + 2n = n(n+1)
Review t test and ANOVA
Part A. Dependent t testIn this assignment, we are interested in finding out whether participation in a creative writing c ...
Review t test and ANOVA
Part A. Dependent t testIn this assignment, we are interested in finding out whether participation in a creative writing course results in increased scores of a creativity assessment. For this part of the assignment, you will be using the data file “Activity 8a.sav”. In this file, “Participant” is the numeric student identifier, “CreativityPre” contains creativity pre-test scores, and “CreativityPost” contains creativity post-test scores. A total of 40 students completed the pre-test, took the creativity course, and then took the post-test.Exploratory Data Analysis/Hypotheses.Perform exploratory data analysis on CreativityPre and CreativityPost. Using SPSS, calculate the mean and standard deviation of these two variables.Construct an appropriate chart/graph that displays the relevant information for these two variables.Write the null and alternative hypotheses used to test the question above (e.g., whether participation in the course affects writing scores).Comparison of MeansPerform a dependent t test to assess your hypotheses above (note that many versions of SPSS use the term “paired samples t test” rather than dependent t test; the test itself is the same.Write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test. Be sure that your writing conforms to APA style.Part B. Independent t testIn this assignment, we will start with the data file used in Part A (“Activity 6a.sav”). Suppose, however, you [the researcher] encountered a small problem during data collection: after the post-tests were collected, you realized that the post-test form did not ask for the students’ identification number. As such, it will be impossible to match pre-test scores to post-test scores. Rather than simply give up, you start thinking about the data you do have, and try to determine whether you can salvage your project. In assessing the situation, you realize that you have 40 pre-test scores and 40 post-test scores, but no way to link them. While it will result in a weaker comparison, you determine that you are still able to compare pre-test vs. post-test scores; you will use a between-subjects design rather than a within-subjects design.Create the data set.Using the “Activity 8a.sav” file as a starting point, create a new dataset that you can use with the between subjects design. Hint: you will no longer need the variables CreativePre and CreativeTest. Instead, you have only one variable for the score on the creativity test. A second (or grouping) variable will serve to indicate which test the student took.Submit the dataset as one of the week’s files. Name the file in the following format: lastnamefirstinitialPSY7107-8b.sav (example: smithbPSY7107-8b.sav).Exploratory Data Analysis/Hypotheses.Comparison of MeansPerform an independent t test to assess your hypotheses above (note that many versions of SPSS use the term “independent samples t test” rather than simply “independent t test”.Write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test. Be sure that your writing conforms to APA style.Comparison of DesignsIn this assignment, you used the same dataset to analyze both a between- and within-subjects design. Create a single paragraph (using the material you wrote above), that presents both sets of results.Explain, in 300-500 words, whether the two tests resulted in the same findings. Did you expect this to be the case? Why or why not? What have you learned in this assignment?Part C. ANOVAAll of us have had our blood pressure measured while at our physician’s office. How accurate are these measurements? It may surprise you to learn that there is something called “white coat syndrome”—the tendency of some people to exhibit elevated blood pressure in clinical (medical) settings only. In other words, for these people the very fact that the physician is taking their blood pressure causes it to increase (for more information about white coat syndrome see http://www.webmd.com/anxiety-panic/features/beyond-white-coat-syndrome ). In this assignment, you will be using the “Activity 8c.sav” data file to determine whether you find support for the existence of white coat syndrome. In this study, 60 participants were randomly assigned to one of three groups. The “settings” variable indicates the location in which the participants’ blood pressure was recorded: 1=home, 2=in a doctor’s office, and 3=in a classroom setting. The “SystolicBP” variable contains the participants’ systolic pressure (the “upper” number). The “DiastolicBP” variable contains the participant’s diastolic pressure (the “lower” number).Exploratory Data Analysis/Hypotheses.Perform exploratory data analysis on both the SystolicBP and DiastolicBP variables. Using SPSS, calculate the mean and standard deviation of these two variables. Be sure that your analysis is broken down by setting (e.g., you will have six means, six SD’s, etc.).Create two graphs—one for systolic and one for diastolic pressure. Each graph should clearly delineate the three groups.Write a null and alternative hypothesis for the comparison of the three groups (note that your hypothesis will state that the three groups are equivalent; be sure to word your null hypothesis correctly).ANOVA.Using the “Activity 8c.sav” data file, perform two single factor ANOVAs: one using SystolicBP and one using DiastolicBP as the dependent variable.If appropriate for either or both of the ANOVAs, perform post hoc analyses to determine which groups actually differ.Write one paragraph for each ANOVA (be sure to use APA style). At a minimum, each paragraph should contain the three means, three SD’s, ANOVA results (F, df), post hoc tests (if applicable), effect size, and an interpretation of these results.Save and name your Word document in the following format: lastnamefirstinitialPSY7107-8.docYou should now have the following files:lastnamefirstinitialPSY7107-8b.sav (example: smithbPSY7107-8b.sav)lastnamefirstinitialPSY7107-8.doc
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module 5 and exam
Problem Set 5.1Problem Set 5.11. Describe, in your own words the sampling distribution of x̄.- Click here to enter answer ...
module 5 and exam
Problem Set 5.1Problem Set 5.11. Describe, in your own words the sampling distribution of x̄.- Click here to enter answer - 2. For the sampling distribution of x̄, is it necessary that the samples used in the distribution be all of the same size?- Click here to enter answer - 3. What is E(x̄)? What is E(x̄) equal to?- Click here to enter answer - 4. Suppose you take a random sample and find the sample mean, x̄. Based on the previous problem, can you say that x̄ is equal to the mean of the entire population µ?- Click here to enter answer - Problem Set 5.2Problem Set 5.21. Suppose that you are attempting to estimate the weight of 600 parts. In order to use the infinite standard deviation formula, what sample size, n, should you use?- Click here to enter answer - 2. A nursing home has 2000 patients. You sample 170 patients. Can you use the infinite standard deviation formula?- Click here to enter answer - 3. Suppose that you take a sample of size 15 from a population that is known to be normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - 4. Suppose that you take a sample of size 20 from a population that is not normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - 5. Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?- Click here to enter answer - Problem Set 5.3Problem Set 5.31. Suppose a pharmaceutical company wants to do a study of the commissions of its sales force. Let's assume that there are 4,300 sales people and the population mean for the sales force is $52,400 in commissions and has a population standard deviation of $3,500. What is the probability that a simple random sample of 50 members of the sales force will have commissions within $400 of the population mean?- Click here to enter answer - 2. Suppose that in a certain large city, the mean 100 meter dash time for male high school seniors was reported to be 13.3 seconds with a standard deviation of 1.9 seconds. We may assume that the population is normally distributed.a) What is the probability that 20 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?- Click here to enter answer - b) What is the probability that 40 male high school seniors selected at random will have a mean 100 meter dash time of 12.5 seconds or less?- Click here to enter answer - c) What is the probability that 35 male high school seniors selected at random will have a mean 100 meter dash time between 13 seconds and 14 seconds?- Click here to enter answer - 3. Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution.a) If you choose 25 potatoes at random, what is the probability that the mean of this sample of 25 potatoes is between 7 and 8 ounces?- Click here to enter answer -b) If you choose 45 potatoes at random, what is the probability that the mean of this sample of 45 potatoes is less than 7 ounces?- Click here to enter answer -c) If you choose 40 potatoes at random, what is the probability that the mean of this sample of 40 potatoes is more than 7.5 ounces?- Click here to enter answer -Problem Set 5.4Problem Set 5.41. According to the American Diabetes Association (2013), 8.3 % of the U.S. population have diabetes.a) Suppose that you take a random of 80 Americans, what is the probability that 7 % or less of these 80 people have diabetes?- Click here to enter answer - b) Suppose that you take a random of 120 Americans, what is the probability that 8 % or more of these 120 people have diabetes?- Click here to enter answer -
2 questions on worksheet.
07.04 Mathematical InductionAssignment Name: ___________________________________Print this page or copy and paste this ass ...
2 questions on worksheet.
07.04 Mathematical InductionAssignment Name: ___________________________________Print this page or copy and paste this assignment in to a word document.After filling in the requested information below, you may either scan your handwritten work or take a clear digital picture. You will need to save the scanned copy or digital picture of your work in order to submit as a file attachment.Note: When saving files, please remember that you should not use a period or a space in your file name. It is recommended that you use the underscore when saving your documents: 1_01, 1_02pg1, 1_02og2, etc. Contact your instructor if you have questions about saving files.Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.(4 points each.)4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 12 + 42 + 72 + ... + (3n - 2)2 = For the given statement Pn, write the statements P1, Pk, and Pk+1.(2 points)2 + 4 + 6 + . . . + 2n = n(n+1)
Review t test and ANOVA
Part A. Dependent t testIn this assignment, we are interested in finding out whether participation in a creative writing c ...
Review t test and ANOVA
Part A. Dependent t testIn this assignment, we are interested in finding out whether participation in a creative writing course results in increased scores of a creativity assessment. For this part of the assignment, you will be using the data file “Activity 8a.sav”. In this file, “Participant” is the numeric student identifier, “CreativityPre” contains creativity pre-test scores, and “CreativityPost” contains creativity post-test scores. A total of 40 students completed the pre-test, took the creativity course, and then took the post-test.Exploratory Data Analysis/Hypotheses.Perform exploratory data analysis on CreativityPre and CreativityPost. Using SPSS, calculate the mean and standard deviation of these two variables.Construct an appropriate chart/graph that displays the relevant information for these two variables.Write the null and alternative hypotheses used to test the question above (e.g., whether participation in the course affects writing scores).Comparison of MeansPerform a dependent t test to assess your hypotheses above (note that many versions of SPSS use the term “paired samples t test” rather than dependent t test; the test itself is the same.Write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test. Be sure that your writing conforms to APA style.Part B. Independent t testIn this assignment, we will start with the data file used in Part A (“Activity 6a.sav”). Suppose, however, you [the researcher] encountered a small problem during data collection: after the post-tests were collected, you realized that the post-test form did not ask for the students’ identification number. As such, it will be impossible to match pre-test scores to post-test scores. Rather than simply give up, you start thinking about the data you do have, and try to determine whether you can salvage your project. In assessing the situation, you realize that you have 40 pre-test scores and 40 post-test scores, but no way to link them. While it will result in a weaker comparison, you determine that you are still able to compare pre-test vs. post-test scores; you will use a between-subjects design rather than a within-subjects design.Create the data set.Using the “Activity 8a.sav” file as a starting point, create a new dataset that you can use with the between subjects design. Hint: you will no longer need the variables CreativePre and CreativeTest. Instead, you have only one variable for the score on the creativity test. A second (or grouping) variable will serve to indicate which test the student took.Submit the dataset as one of the week’s files. Name the file in the following format: lastnamefirstinitialPSY7107-8b.sav (example: smithbPSY7107-8b.sav).Exploratory Data Analysis/Hypotheses.Comparison of MeansPerform an independent t test to assess your hypotheses above (note that many versions of SPSS use the term “independent samples t test” rather than simply “independent t test”.Write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test. Be sure that your writing conforms to APA style.Comparison of DesignsIn this assignment, you used the same dataset to analyze both a between- and within-subjects design. Create a single paragraph (using the material you wrote above), that presents both sets of results.Explain, in 300-500 words, whether the two tests resulted in the same findings. Did you expect this to be the case? Why or why not? What have you learned in this assignment?Part C. ANOVAAll of us have had our blood pressure measured while at our physician’s office. How accurate are these measurements? It may surprise you to learn that there is something called “white coat syndrome”—the tendency of some people to exhibit elevated blood pressure in clinical (medical) settings only. In other words, for these people the very fact that the physician is taking their blood pressure causes it to increase (for more information about white coat syndrome see http://www.webmd.com/anxiety-panic/features/beyond-white-coat-syndrome ). In this assignment, you will be using the “Activity 8c.sav” data file to determine whether you find support for the existence of white coat syndrome. In this study, 60 participants were randomly assigned to one of three groups. The “settings” variable indicates the location in which the participants’ blood pressure was recorded: 1=home, 2=in a doctor’s office, and 3=in a classroom setting. The “SystolicBP” variable contains the participants’ systolic pressure (the “upper” number). The “DiastolicBP” variable contains the participant’s diastolic pressure (the “lower” number).Exploratory Data Analysis/Hypotheses.Perform exploratory data analysis on both the SystolicBP and DiastolicBP variables. Using SPSS, calculate the mean and standard deviation of these two variables. Be sure that your analysis is broken down by setting (e.g., you will have six means, six SD’s, etc.).Create two graphs—one for systolic and one for diastolic pressure. Each graph should clearly delineate the three groups.Write a null and alternative hypothesis for the comparison of the three groups (note that your hypothesis will state that the three groups are equivalent; be sure to word your null hypothesis correctly).ANOVA.Using the “Activity 8c.sav” data file, perform two single factor ANOVAs: one using SystolicBP and one using DiastolicBP as the dependent variable.If appropriate for either or both of the ANOVAs, perform post hoc analyses to determine which groups actually differ.Write one paragraph for each ANOVA (be sure to use APA style). At a minimum, each paragraph should contain the three means, three SD’s, ANOVA results (F, df), post hoc tests (if applicable), effect size, and an interpretation of these results.Save and name your Word document in the following format: lastnamefirstinitialPSY7107-8.docYou should now have the following files:lastnamefirstinitialPSY7107-8b.sav (example: smithbPSY7107-8b.sav)lastnamefirstinitialPSY7107-8.doc
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