Brigden was told, "You can average $76 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of $3.35. Over the first 38 days she was employed at the restaurant, the mean daily amount of her tips was $79.58. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $76?

State the null hypothesis and the alternate hypothesis.

A. H0: μ > 76 ; H1: μ = 76
B. H0: μ ≥ 76 ; H1: μ < 76
C. H0: μ ≤ 76 ; H1: μ > 76
D. H0: μ = 76 ; H1: μ ≠ 76

Option c) is the correct answer. The correct null hypothesis for Ms. Brigden's case is that the population mean is less than or equal to $76 (H0: μ ≤ 76) and the alternative hypothesis is that the population mean is greater than $76 (H1: μ > 76).

Explanation:

In hypothesis testing, the null hypothesis (H0) is a statement of no effect or no difference and is assumed to be true until evidence suggests otherwise. The alternative hypothesis (H1 or Ha) indicates the possibility of an effect or difference that the test seeks to support.

Given that Ms. Brigden wants to determine if her daily tips average more than $76, the null hypothesis should reflect the status quo or the established average, while the alternative hypothesis should reflect the claim that her average tips are greater than this established average:

H0: μ ≤ 76 (The population mean is less than or equal to $76)
H1: μ > 76 (The population mean is greater than $76)

So, the correct hypotheses for Ms. Brigden's case would be:

H0: μ ≤ 76 ; H1: μ > 76