Question

# At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden...

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

1. 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

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

Value of the test statistic _____

1. What is your decision regarding H0?
• Do not reject H0

• Reject H0

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

a) Option-C) H0: μ ≤ 70; H1: μ > 70

b) critical value = Z0.02 = 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

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