Statistics Exam: Parameter Estimation and Hypothesis Testing

Scenario 1: Obesity among City Residents

Instructions: Download this pdf and complete it as you have been doing with the Explorations. The completed pdf must be uploaded by 8 am (central time) on Saturday, 18 Sep. The submission link will close at that time. All exams must be submitted through the Canvas submission link. Any exam submitted via email or Canvas messenger will be deleted. The Canvas submission link will allow you to submit more than one document. At two places in the exam, you’re asked to submit screenshots. These may be uploaded as separate files in the submission link; you don’t need to try to append them to this pdf. 1. A study conducted by the National Center for Health Statistics as part of the Center for Disease Control and Prevention (CDC) found that, as of 2015-2016, 39.6% of Americans over the age of 20 fit the medical definition of being obese (BMI of 30 or higher). A city known for its plentiful outdoor opportunities believes that number is lower among its residents. A representative sample of 80 city residents is collected and the BMI calculated for each (based on reported height and weight). The variable of interest is whether the resident fit the medical definition of obese. The study found 22 people in the sample fit the medical definition of obese. (a)  What does the parameter represent in the context of this scenario? Use both a symbol and words (b) Write the null and alternative hypotheses that will answer the researchers’ question. Write the hypotheses in words. (c) Carry out the appropriate simulation-based test using the applet, and report the following: i. The resulting p-value: ii The resulting standardized statistic: 2 iii. Take a screenshot of the applet with the p-value and summary statistics included, and upload the screenshot to the submission link. Make sure that all values you entered into the applet are readable, i.e., that the picture is not so small that we can’t see what values you’ve entered. (d)Based on the evidence you found in (d), answer the researchers’ question. Make sure to clearly state your decision and summarize the results in context. 3 2. Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? (a)What does the parameter represent in the context of this scenario? Use both a symbol and words. (b) Write the null and alternative hypotheses that are of interest in this scenario. Write the hypotheses in words. (c) Carry out the appropriate theory-based test using the applet, and report the following: i.  The resulting p-value: ii. The resulting standardized statistic: iii. Take a screenshot of the applet with the p-value and summary statistics included, and upload the screenshot to the submission link. Make sure that all values you entered into the applet are readable, i.e., that the picture is not so small that we can’t see what values you’ve entered. (d)  Based on the evidence you found in (d), answer the research question. Make sure to clearly state your decision and summarize the results in context