The speed with which consumers decide to purchase a product was investigated by a group of researchers. The researchers hypothesized that consumers with last names that begin with letters later in the alphabet and consumers with last names that begin with letters earlier in the alphabet will tend to acquire items at different speeds (called the last name effect). A random sample of 30 individuals from each set of last names was selected. The groups are defined as (1) having a last name that starts with the first nine letters of the alphabet (A – I) and (2) having a last name that begins with the last nine letters of the alphabet (R – Z). Each group was offered the same unbelievable deal on a popular item and the response time to purchasing the item was measured in minutes. It is known that the two population distributions of purchase times are normally distributed. Use the following sample statistics to complete this problem.

Statistics/Drinkware

A - I

R - Z

Sample size, n

30

30

Sample mean, x

25.08

19.38

Sample standard deviation, s

10.41

7.12

Define the population parameter of interest in context of this question in one sentence.
Construct the 95% confidence interval in StatCrunch using STAT à T Stats à Two Sample à With Summary. Copy and paste the output table into your document.
Imagine you were using a hypothesis test to determine if a significant difference exists in the purchase times. State the hypotheses you would use to test this hypothesis.
What decision and conclusion can be made in this case? Provide an answer and a reason for your choice in one or two sentences. Please only use your confidence interval to answer this question (do not run this hypothesis test in this part).
Produce hypothesis test output using STAT à T Stats à Two Sample à With Summary and verify your decision in part (d).
Construct the 99% confidence interval in StatCrunch using STAT à T Stats à Two Sample à With Summary. Copy and paste the output table into your document.
Using the same hypotheses you stated in part (c), what decision and conclusion can be made in this case? Provide an answer and a reason for your choice in one or two sentences. Please only use your confidence interval to answer this question (do not run this hypothesis test in this part).