statistics-187
statistics-187
1. A sample of 47 observations is selected from a normal population. The sample mean is 30, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 29
H1 : μ > 29
a. Is this a one- or two-tailed test?
“One-tailed”-the alternate hypothesis is greater than direction.
“Two-tailed”-the alternate hypothesis is different from direction.
b. What is the decision rule? (Round your answer to 3 decimal places.)
H0, when z >
c. What is 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
Reject
There is evidence to conclude that the population mean is greater than 29.
e. What is the p-value? (Round your answer to 4 decimal places.)
p-value
2.At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $83 a day in tips.†Assume the population of daily tips is normally distributed with a standard deviation of $4.07. Over the first 45 days she was employed at the restaurant, the mean daily amount of her tips was $84.86. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $83?
a. State the null hypothesis and the alternate hypothesis.
H0: μ = 83 ; H1: μ ≠83
H0: μ ≥ 83 ; H1: μ < 83
H0: μ ≤ 83 ; H1: μ > 83
H0: μ >83 ; H1: μ = 83
b. State the decision rule.
Reject H1 if z < 1.65
Reject H0 if z < 1.65
Reject H1 if z > 1.65
Reject H0 if z > 1.65
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?
Reject H0
Do not reject H0
e. What is the p-value? (Round your answer to 4 decimal places.)
p-value
