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# Hypothesis testing using either t or normal distribution

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1. A sample of 49 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H0 : μ ≤ 20
H1 : μ > 20

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?

Reject
Do not reject

There is evidence to conclude that the population mean is greater than 20.

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 \$89 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of \$2.81. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was \$92.66. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than \$89?

a. State the null hypothesis and the alternate hypothesis.

H0: μ ≥ 89 ; H1: μ < 89
H0: μ ≤ 89 ; H1: μ > 89
H0: μ = 89 ; H1: μ ≠ 89
H0: μ >89 ; H1: μ = 89

b. State the decision rule.

Reject H1 if z > 2.33
Reject H0 if z < 2.33
Reject H0 if z > 2.33
Reject H1 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?

Reject H0
Do not reject H0

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

p-value

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 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 25 sales representatives reveals that the mean number of calls made last week was 43. The standard deviation of the sample is 2.8 calls. Using the 0.010 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?

H0 : μ ≤ 41
H1 : μ > 41

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

Value of the test statistic

4. A United Nations report shows the mean family income for Mexican migrants to the United States is \$26,580 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 26 Mexican family units reveals a mean to be \$38,900 with a sample standard deviation of \$11,054. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

a. State the null hypothesis and the alternate hypothesis.

5. The following information is available
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.)

Reject H0 if t is not between
and

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

Value of the test statistic

5. The following information is available.
H0 : μ ≥ 220

H1 : μ < 220

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?

Two-tailed test
One-tailed test

b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

H0 when z <

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.)

Value of the test statistic

d. What is your decision regarding H0?

Reject
Do not reject

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

p-value

6. Given the following hypotheses:

H0 : μ ≤ 10
H1 : μ > 10

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.)

Reject H0 if t >

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

Value of the test statistic

7. Given the following hypotheses:

H0 : μ = 400

H1 : μ ≠ 400

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.)

Reject H0 when the test statistic is the interval (
,
).

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

Value of the test statistic

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-normal-distribution-624340

#### Solution Preview

1. A sample of 49 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 20
H1 : μ > 20
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 >1.645
c. What is the value of the test statistic? (Round your answer to 2 decimal places.)
Value of the test statistic=(21-20)/[4/sqrt(49)]=1.75
d. What is your decision regarding H0?
Reject
Do not reject
There is evidence to conclude that the population mean is greater than 20.
e. What is the p-value? (Round your answer to 4 decimal places.)
p-value=P(Z>1.75)=0.0401
2. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average \$89 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of \$2.81. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was \$92.66. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than \$89?
a. State the ...

#### Solution Summary

The solution gives detailed solutions to a series of questions on hypothesis testing using either t or normal distribution following formal 5 steps.

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