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### Course: AP®︎/College Statistics>Unit 11

Lesson 5: Testing for the difference of two population means

# Test statistic in a two-sample t test

## Problem

Mio, a restaurant owner, wants to test if her two managers perform at the same level. To do that, she collects data about the number of customer complaints at two random samples of shifts (one for each manager). Here is a summary of the results:
Manager AManager B
Mean$4$ complaints$5$ complaints
Standard deviation$0.3$ complaints$0.5$ complaints
Number of shifts$19$$21$
Mio wants to use these results to carry out a two-sample $t$ test to determine if the mean numbers of complaints are significantly different for the two managers. Assume that all conditions have been met.
Which of the following would be an appropriate test statistic for Mio's test?