Data Analysis Assignment in Statistics

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timer Asked: May 4th, 2017

Question description

Please, follow the instructions on the word document and provide detailed answers if needed in the short answer questions.

Data Analysis Assignment #4 Spring 2017 STAT 250 Your submitted document should include the following items. Points will be deducted if the following are not included: 1. Type your Name, STAT 250 with your correct section number (e.g. STAT 250-xxx) and Data Analysis Assignment #4 centered on the top of page 1 of your document. 2. Number your pages across your entire solutions document. 3. Your document should include the ANSWERS ONLY to the following FOUR questions with each answer labeled by its corresponding number and subpart. Keep the questions in order. Do NOT include the questions in your submitted document. 4. Generate all requested graphs and tables using StatCrunch. 5. Upload your document onto Blackboard as a Word or pdf document using the link provided by your instructor. Elements of good technical writing: Use complete and coherent sentences to answer the questions. Graphs must be appropriately titled and should refer to the context of the question. Graphical displays must include labels with units if appropriate for each axis. Units should always be included when referring to numerical values. When making a comparison you must use comparative language, such as “greater than”, “less than”, or “about the same as.” Ensure that all graphs and tables appear on one page and are not split across two pages. Show all mathematical calculations when directed to compute an answer ‘by-hand.’ When writing mathematical expressions into your document you may use either an equation editor or common shortcuts such as: x can be written as sqrt(x), p̂ can be written as p-hat, x can be written as x-bar. 1 Instructions Questions #1-#3 will use the results from a survey administered to a nationwide random sample of high school students found in our StatCrunch group titled CensusAtSchool. For this assignment we will consider the survey results as a random sample of all U.S. high school students. Question #4 will require you to enter a data set into StatCrunch. Question 1 The CensusAtSchool data set contains results from a survey question in which students were asked “What is your length of your armspan in centimeters?” 1a. Use StatCrunch to construct an appropriately titled and labeled boxplot for the variable, Armspan_cm. Remember to select “Use fences to identify outliers” and “Draw boxes horizontally.” 1b.Use StatCrunch to find the sample size, mean, median and standard deviation for the variable, Armspan_cm, using Stat->Summary Statistics->Columns. Copy and paste your results into your document and then round the mean and standard deviation to two decimal places in the table. 1c. Describe the distribution (i.e., shape, center, spread and outliers) of this variable as shown by both your boxplot and your descriptive statistics. 1d. Verify that all three conditions for conducting statistical inference have been met. Show any required calculations. 1e. Construct “by-hand” a 95% confidence interval for the mean arm span length in centimeters for all U.S. high school students. Show all work including the formula. Your final answer should be written as statistic ± margin of error AND in interval notation (lower limit, upper limit). All answers should be rounded to two decimal places). Note: Use t*=1.96 as the sample size is so large. 1f. Use StatCrunch to verify your 95% confidence interval for the mean armspan length in centimeters for all U.S. high school students using the steps below. Note: you may see slight differences in values between StatCrunch and your hand calculations due to computer precision. Step 1: Stat -> T Stats -> One Sample -> With Data Step 2: Follow the directions below to enter the correct information Copy and paste the result into your document. 1g. Interpret this confidence interval, using your output from part 1f, in a complete sentence in the context of the question. Round your answer to two decimal places. 2 Question 2 Do females value the importance of recycling more than males? We will use the results from the CensusAtSchool data set to investigate this question. Assume all conditions for conducting inference have been met for this question. 2a. Use StatCrunch to find the sample size, mean, and standard deviation for the importance of recycling rubbish, variable Importance_recycling_rubbish , reported separately for males and females in the CensusAtSchool data set. Copy and paste your results into your document and then round these values in two decimal places in the copied table. Note: Remember to use group by: Gender. 2b. State the null and alternative hypotheses to test if females (group 1) reported a higher average score for the importance of recycling rubbish than males (group 2). Remember to define all parameters of interest. 2c. Use the information from part 2a to calculate ‘by-hand’ the value of the test statistic to two decimal places. Show all work and the formula. 2d. Use StatCrunch to verify your result by following the steps below. Step 1: Stat-> T Stats -> Two Sample -> With Data Step 2: Follow the directions below to enter the correct information Copy and paste the result into your document. WARNING CASE SENSITIVE: Both variable name and variable value WARNING: Uncheck this box! Enter the appropriate alternative hypothesis information <, > or ≠ in this box. 2e. Using a significance level of 0.05 and the p-value in part 2d, should the null hypothesis be rejected? 2f. In a sentence, write the conclusion of this test in the context of the researcher’s question. 3 Question 3 Do females and males equally value the importance of internet access at home? We will use the results from the CensusAtSchool data set to investigate this question. Assume all conditions for conducting inference have been met for this question. 3a. Use StatCrunch to find the sample size, mean and standard deviation for the variable Importance_Internet_access reported separately for both males and females. Copy and paste your results into your document and then round these values in two decimal places in the table. Note: Remember to use group by: Gender. 3b. Use the information from part 3a to construct a 95% confidence interval ‘by-hand’ for the difference between the means for males and females (males-females) on the variable Importance_Internet_access. Show all work and the formula. Note: Use t*=1.96 as both sample sizes are so large. Report your confidence interval in both formats: statistic +/- margin for error and (lower limit, upper limit) rounded to two decimal places. 3c. Now use Statcrunch to construct a 95% confidence interval by following the steps below. Copy and paste the results into your document. Step 1: Stat-> T Stats -> Two Sample -> With Data Step 2: Select the Variable: Importance_Internet_access Split by Gender (as shown below) Select Confidence interval Level:0.95 Uncheck this box! 3d. In a complete sentence, interpret the confidence interval results from part 3c in the context of the question. 3e. Use your confidence interval results from part 3c to determine if you should reject or fail to reject the null hypothesis if you had decided to conduct a two-sided hypothesis test instead of creating a confidence interval to determine if there was a difference in the means for males and females for the variable Importance_Internet_access. Justify your decision in a sentence using your confidence interval. 4 Question 4 A tire manufacturer tested the braking performance of one of its tire models on a test track. Ten cars made stops from 60 miles per hour on both wet and dry pavement. The stopping distances in feet were recorded and are shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Wet Pavement 211 191 220 207 198 208 206 177 186 223 Dry Pavement 145 152 141 143 131 148 126 140 135 133 4a. The researcher wants to use this data to determine if the stopping distance on wet pavement is greater than the stopping distance on dry pavement. The researchers used a paired research design as shown in the data set above. Explain why this format is a called a paired design. 4b. State the null and alternative hypothesis for this test. Define the parameter of interest. 4c. Enter this data set into Statcrunch using a new (empty) data table. You can select “New Data Table” under the StatCrunch tab. Once you have entered the data, select Stat-> T Stats -> Paired using ‘wet pavement’ as sample 1 and ‘dry pavement’ as sample 2. Copy and paste both the output and boxplot into your document. Note: As a check of your data entry, the sample mean difference should equal 63.3. Check This Box: Save Differences Select appropriate symbol Select Boxplot with mean marker 4d. As the researcher used a very small sample size we must verify that the distribution of differences is Normally distributed. Use your boxplot to verify that this condition has been satisfied. 4e. Make a decision concerning your hypothesis test using a significance level of 0.05. 4f. State your conclusion in the context of the question. 5

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