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# testing for difference in means with a z-statistic.

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Identify the test and state the hypothesis, then:

Katy Fit, aerobics instructor at the Anderson Recreation Center, is analyzing the attendance at her classes. She wonders if the mean number of people who come on Monday morning is the same as on Wednesday morning. Some people may be exhausted from their other weekend activities and skip Mondays. Yet others may get busy midweek and be unable to fit exercise into their schedules. Summary data for 35 randomly selected Mondays and 35 randomly selected Wednesdays are reported below. Is there a significant difference in the mean numbers of people who come to class on the two days?
a. Use the P-value method to perform the appropriate test at the 0.04 level of significance.
(Yes, I mean 0.04; it is not a typo.)

b. Find the 95% confidence interval for the difference between the two means.

Sample 1: Monday: Mean = 35 s = 9.5 n = 35
Sample 2: Wednesday: Mean = 28.5, s = 9.8 n = 35