Pauly’s Pizza claims that the mean time it takes for them todeliver a pizza to dorms at Nat’s college is 31 minutes. After along wait one night, Nat decides to test this claim. He randomlyselects 15 dormitory residents and asks them to record the time ittakes for Pauly’s to deliver the next time they order pizza. Hereare the results (in minutes). The sample mean is x=33.8 and thesample standard deviation is s= 7.72 .
31 38 39 25 26 45 42 32 23 38 42 21 40 37 28
a. We want to use this information to construct a 90% confidenceinterval to estimate the true mean delivery time. State theparameter our confidence interval will estimate (in context).
b. Identify the conditions that must be met to use thisprocedure and explain how you know that each one has beensatisfied. For the Nearly Normal Condition, include a picture ofthe histogram of the sample data. Make sure to include labels.Hint: Start the distribution from 20 and use a bin width of 4.
c. Find the appropriate critical value () and the standard errorof the sample mean (). SHOW YOUR WORK! Round the standard error totwo decimal places.
d. Use the formula shown in your notes to get the 90% confidenceinterval by hand. SHOW YOUR WORK! Round to one decimal places.
e. Interpret the confidence interval constructed in part (d) inthe context of the problem.
f. Interpret the confidence level in the context of theproblem.
g. Suppose you wanted to estimate the mean delivery time toNat’s college with 90% confidence to have a margin of error no morethan 5 minutes. Calculate how large a sample you would need. Assumemin. SHOW YOUR WORK! Remember to round your final answer UP to thenearest whole number.
h. Recall that Pauly’s Pizza claimed the average time it wouldtake to deliver to Nat’s college is 31 minutes. Does your 95%confidence interval support this claim?
i. What is the name of the significance test that can we performto test the claim made?
j. What hypotheses would we use if we wished to conduct atwo-sided test?
k. Calculate the t-score using the formula shown in class. Roundto two decimal places. SHOW YOUR WORK! l. Use your t-score (withcorresponding degrees of freedom) to estimate the p-value with ourt-table. m. It turns out the exact p-value is 0.182. Interpret thep-value in context.
n. What decision would you draw based on the size of thep-value?
o. Are our confidence interval and significance test results inagreement?
