1. A sample of 37 observations is selected from a normal population. The sample mean is 29, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 26
H1 : μ > 26
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.)
d. What is your decision regarding H0?
There is evidence to conclude that the population mean is greater than 26.
e. What is the p-value? (Round your answer to 4 decimal places.)
2. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average $82 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of $3.26. Over the first 44 days she was employed at the restaurant, the mean daily amount of her tips was $84.61. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $82?
a. State the null hypothesis and the alternate hypothesis.
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H0: μ ≥ 82 ; H1: μ < 82
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H0: μ = 82 ; H1: μ ≠ 82
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H0: μ >82 ; H1: μ = 82
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H0: μ ≤ 82 ; H1: μ > 82
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b. State the decision rule.
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Reject H1 if z > 2.05
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Reject H0 if z < 2.05
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Reject H0 if z > 2.05
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Reject H1 if z < 2.05
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c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
d. What is your decision regarding H0?
e. What is the p-value? (Round your answer to 4 decimal places.)
3. The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 39 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 29 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.4 calls. Using the 0.050 significance level, can we conclude that the mean number of calls per salesperson per week is more than 39?
H0 : μ ≤ 39
H1 : μ > 39
a. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
b. What is your decision regarding H0?
H0. The mean number of calls is than 39 per week.
4. United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 28 Mexican family units reveals a mean to be $34,120 with a sample standard deviation of $10,050. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
a. State the null hypothesis and the alternate hypothesis.
H0: μ =
H1: μ ≠
b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
d. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
The following information is available.
H0 : μ ≥ 220
H1 : μ < 220
5. A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.
a. Is this a one- or two-tailed test?
b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
d. What is your decision regarding H0?
e. What is the p-value? (Round your answer to 4 decimal places.)
H0 : μ ≤ 10
H1 : μ > 10
6. A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level:
a. State the decision rule. (Round your answer to 3 decimal places.)
b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
c. What is your decision regarding the null hypothesis?
H0. There is evidence to conclude that the population mean is greater than 10
H0 : μ = 400
H1 : μ ≠ 400
7. A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:
a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
c. What is your decision regarding the null hypothesis?