Question

Sample Statistic	Value of sample statistic
Sample mean () Body Mass Index (BMI)	21.65
Sample standard deviation (s) of Body Mass Index (BMI)	4.33
Sample size	92

1. (13 points) You will use information about the body mass index (BMI) variable for the sample of adolescent girls to perform a hypothesis test. You will test the claim that the mean BMI for all adolescent girls is 21.0.
   1. The null hypothesis is H₀ : µ = 21.0. State the alternate hypothesis for a two-sided test.
   2. First, check that the conditions are met for this hypothesis test. You can assume that the collected data is a random sample.
   3. Calculate the test statistic for this hypothesis test using the appropriate formula. Note that the population standard deviation is unknown. YOU MUST SHOW ALL WORK IN YOUR DOCUMENT TO RECEIVE FULL CREDIT. Round any values that you use to three decimal places.
   4. Determine the p-value for this hypothesis test using the Standard Normal Table (Z table). State the p-value as a decimal to four decimal places.
   5. Draw a conclusion for this hypothesis test and give the reason for your conclusion. Use a level of significance of α = .05.
   6. Based on the given information, compute a 95% confidence interval for the population mean BMI of adolescent girls. Note that you were asked to do this in Minitab Assignment 5, so you can use your answer from that assignment. SHOW ALL WORK IN YOUR DOCUMENT for this 95% confidence interval for the population mean BMI of adolescent girls.
   7. Is the value of 21.0 contained in your confidence interval? Does this make sense? Why?

Answer 1