Question

Problem 2: Pizza Prices in Different Cities (no data set in StatCrunch)
A food blogger is interested in comparing the price of pizzas available for purchase in New York City to those available in Washington, D.C. To do so, they collected a random sample of 30 large cheese pizzas from each of the cities. The New York pizzas had an average price of $12.83 with a standard deviation of $4.45. The Washington, D.C. pizzas had an average price of $10.71 with a standard deviation of $3.74. At the 0.01 significance level, can the blogger conclude that the mean price of a large cheese pizza in New York is higher than Washington, D.C.? Assume all conditions for conducting inference are satisfied.

a) Conduct a full hypothesis test by following the steps below. Enter an answer for each of these steps in your document. i. Define the population parameter of interest in context of this question in one sentence. ii. State the null and alternative hypotheses using correct notation. iii. State the significance level for this problem. iv. Calculate the test statistic in StatCrunch using STAT  T Stats  2 Sample  With Summary. Copy and paste the output table into your document. v. Label the p-value seen in your output table produced in part (iv) using the proper probability notation (it begins with P(…)). vi. State whether you reject or do not reject the null hypothesis and your reason for your answer in one sentence. vii. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

b) Imagine if the significance level for this problem was 0.05. State your decision and conclusion for the above hypothesis test when you compare your p-value found in part (v) with the significance level of 0.05.

Answer 1