Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told. “You can average more than $80 a day in tips.” Assume the standard deviation of the population distribution is $3.24. Over the first 36 days that she was employed at the restaurant, the mean daily amount of her tips was $81.35. Calculate the P value. At the 0.01 significance level, can Ms. Brigden conclude that she is earning an average of more than $80 in tips?

Answer 1

H₀: = 80

H₁: > 80

The test statistic z = ()/()

                              = (81.35 - 80)/(3.24/sqrt(36))

                              = 2.5

P-value = P(Z > 2.5)

              = 1 - P(Z < 2.5)

              = 1 - 0.9938

             = 0.0062

Since the P-value is less than the significance level (0.0062 < 0.01), so we should reject the null hypothesis.

At 0.01 significance level Ms. Brigden can conclude that she is earning an average of more than $80 in tips.