At the time she was hired as a server at the Grumney Family Restaurant, Beth Bri

Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $81 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.46. Over the first 43 days she was employed at the restaurant, the mean daily amount of her tips was $82.20. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $81? a. State the null hypothesis and the alternate hypothesis. H0: >81 ; H1: = 81 H0: 81 ; H1: > 81 H0: 81 ; H1: < 81 H0: = 81 ; H1: 81 b. State the decision rule. Reject H0 if z < 2.33 Reject H1 if z > 2.33 Reject H1 if z < 2.33 Reject H0 if z > 2.33 c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Do not reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.) p-value

Explanation / Answer

a) H0: mu <=81 (average daily tips is at most 81)

H1: mu>81 (average daily tips is more than 81).

b) Compute z test statistic.

z=(Xbar-mu)/(s/sqrt N)=(82.20-81)/(3.46/sqrt 43)=2.27

Reject H0, if z (obtained)> z(critical) that is reject H0 if z>2.33.

here, z (obtained) do not fall in critical region. Therefore, fail to reject null hypothesis.

p value is 0.0116.

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