Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $70 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.46. Over the first 32 days she was employed at the restaurant, the mean daily amount of her tips was $71.08. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $70?

1. State the null hypothesis and the alternate hypothesis.

• H₀: μ ≥ 70; H₁: μ < 70

• H₀: μ >70; H₁: μ = 70

• H₀: μ ≤ 70; H₁: μ > 70

• H₀: μ = 70; H₁: μ ≠ 70

2. State the decision rule.

• Reject H₀ if z > 2.05

• Reject H₁ if z < 2.05

• Reject H₁ if z > 2.05

• Reject H₀ if z < 2.05

3. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic _____

4. What is your decision regarding H₀?

• Do not reject H₀

• Reject H₀

5. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

a) Option-C) H₀: μ ≤ 70; H₁: μ > 70

b) critical value = Z_0.02 = 2.05

Option-A) Reject H₀ if z > 2.05

c) Test statistic

                        

                         = 1.77

d) Option-A) Do not reject H₀

e) p-value = P(Z > 1.77) = 1 - P(Z < 1.77) = 1 - 0.9616 = 0.0384