A restaurant chain is interested determining the mean number of times college st
ID: 3225195 • Letter: A
Question
A restaurant chain is interested determining the mean number of times college students eat out each week. We will use our class data as a sample of all college students. In our class (n=16), the mean number of times people ate meals away from the home was 3 with an SD of 1.5. 1. Examine the assumptions and conditions needed to use the t distribution for the sampling distribution of the sample mean number of times a group of college students eat out each week. Complete the following even if the assumptions and conditions aren't met. 2. Create a 90% confidence interval for the mean number of times a group of college students eats out each week. Show your work or describe how you used your calculator to arrive at the answer. 3. Interpret your confidence interval. 4. Write hypotheses to test the assertions that the average number of times a group of college students dines out each week is equal to 5 vs the average number of times a group of college students dines out each week is less than 5. 5. Calculate a p-value for the hypothesis test. Show your work or describe how you used your calculator to arrive at the answer. 6. What is your conclusion at the 0.01 significance level?
Explanation / Answer
1) Since sample size is small (n < 30), Hence T distribution is suitable in this context
2) 90% Confidence interval = [xbar ± T critical *s/n]
= [3 ± 1.753 * 1.5/16]
= [2.343, 3.657]
3) It is 90% confident that true mean number of times college students eat out each week lies in the above interval.
4) H0: µ = 5
H1: µ < 5
5) p value = p [T < xbar - µ / [s/n]]
= p [T < -5.333]
= 0.0001
6) Decision rule : If p value < 0.01, then reject H0
Now Reject H0, since p value < 0.01