A shoe salesman wishes to check the validity of his supplier's claim that the average length of the adult male foot is 9.34 in.He randomly samples 35 adult male customers and finds their average foot length to be 9.01 in.The standard deviation of foot length is known to be 0.75 in.What would be the test statistic for this test if the salesman thinks the supplier's claim is too high?
A) 2.60
B) -0.44
C) 0.44
D) -2.60

Question

Quizplus · Accepted Answer

The test statistic can be calculated as:
t = (sample mean - hypothesized mean) / (standard deviation / square root of sample size)
Here, the hypothesized mean is 9.34 (supplier's claim), the sample mean is 9.01, the standard deviation is 0.75, and the sample size is 35. 
t = (9.01 - 9.34) / (0.75 / sqrt(35))
t = -2.60
Since the salesman thinks the supplier's claim is too high, he is conducting a one-tailed test with the alternative hypothesis being that the true mean is less than 9.34. Therefore, we look at the left tail of the t-distribution with 34 degrees of freedom (n-1). Using a t-table or t-distribution calculator, we find that the critical value for a one-tailed test with alpha = 0.05 and 34 degrees of freedom is -1.690. Since our calculated t-value of -2.60 is more extreme than the critical value of -1.690, we reject the null hypothesis and conclude that there is evidence to suggest that the true mean foot length of adult males is less than 9.34 inches.

A Shoe Salesman Wishes to Check the Validity of His