# Testing Hypotheses and Confidence Intervals

A random sample of size 64 has sample mean 24 and sample standard deviation 4.

d. Is it appropriate to use the t distribution to compute a confidence interval for the population mean? Why or why not?

e. Construct a 95% confidence interval for the population mean.

f. Explain the meaning of the confidence interval you just constructed.

How much do adult male grizzly bears weigh in the wild? Six adult males were captured, tagged and released in California and here are their weights:

480, 580, 470, 510, 390, 550

g. What is the point estimate for the population mean?

h. Construct at 90% confidence interval for the population average weight of all adult male grizzly bears in the wild.

i. Interpret the confidence interval in the context of this problem.

After going to a fast food restaurant, customers are asked to take a survey. Out of a random sample of 340 customers, 290 said their experience was "satisfactory." Let p represent the proportion of all customers who would say their experience was "satisfactory."

j. What is the point estimate for p?

k. Construct a 99% confidence interval for p.

l. Give a brief interpretation of this interval.

Suppose the p-value for a right-tailed test is .0245.

a. What would be your conclusion at the .05 level of significance?

b. What would the p-value have been if it were a two-tailed test?

A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation is 1.5. Use a level of significance of 0.02 to conduct a left-tailed test of the claim that the population mean is 10.0.

a. Are the requirements met to run a test like this?

b. What are the hypotheses for this test?

c. Compute the test statistic and the p-value for this test.

d. What is your conclusion at the 0.02 level of significance?

MTV states that 75% of all college students have seen at least one episode of their TV show "Jersey Shore". Last month, a random sample of 120 college students was selected and asked if they had seen at least one episode of the show. Out of the 120, 85 of them said they had seen at least one episode. Is there enough evidence to claim the population proportion of all college student that have watched at least one episode is less than 75% at the 0.05 level of significance?

a. Are the requirements met to run a test like this?

b. What are the hypotheses for this test?

c. Compute the test statistic and the p-value for this test.

d. What is your conclusion at the 0.05 level of significance?

https://brainmass.com/statistics/hypothesis-testing/testing-hypotheses-and-confidence-intervals-587468

#### Solution Summary

The solution gives detailed answers for a set of 4 questions on performing hypothesis testing, constructing confidence intervals and interpreting p-value.

Confidence Intervals for mean; t test; hypothesis test for proportion

Confidence intervals/One sample hypothesis tests

Directions: For #1, calculate and interpret the confidence interval. Please show your manual calculation or the software output. Please show your work if you calculated manually on #1. If you used statistical software, please show the output.

1: Confidence Intervals for the mean:

A researcher is studying stress among executives. The researcher is using a questionnaire that measures stress. The questionnaire has been validated through past use. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores.

94

88

73

90

68

79

87

95

87

92

83

94

82

85

84

What is the 95% confidence level? Do you conclude that the executives have a dangerous level of stress? Why?

For #2, which is a one-sample test, identify the null and alternative hypothesis, and the critical value. Then, calculate or identify the test statistic, and make a decision on the null hypothesis. Explain why you made your decision on the null hypothesis

2: Hypothesis test for the population mean: t test

An electronics manufacturing process has a scheduled mean completion time of minutes. It is claimed that, under new management, the mean completion time, , is less than minutes. To test this claim, a random sample of completion times under new management was taken.

The sample had a mean completion time of minutes and a standard deviation of minutes. Assume that the population of completion times under new management is normally distributed. At the level of significance, can it be concluded that the mean completion time, , under new management is less than the scheduled mean?

Perform a one-tailed test.

Hypothesis Test: Mean vs. Hypothesized Value

70.00 hypothesized value

66.00 mean Q1

10.00 std. dev.

2.77 std. error

13 n

12 df

-1.44 t

.0874 p-value (one-tailed, lower)

59.96 confidence interval 95.% lower

72.04 confidence interval 95.% upper

6.04 half-width

1: State the null & alternative hypothesis:

2: Identify the critical value

3: Identify the test statistic

4: State and explain your decision on H0

For #3, which is a one-sample test, identify the null and alternative hypothesis, and the critical value. Then, calculate or identify the test statistic, and make a decision on the null hypothesis. Explain why you made your decision on the null hypothesis

3: Hypothesis test for a population proportion

The manufacturer of a new antidepressant claims that, among all people with depression who use the drug, the proportion of people who find relief from depression is at least . A random sample of patients who use this new drug is selected, and of them find relief from depression. Based on these data, can we reject the manufacturer's claim at the level of significance?

Perform a one-tailed test.

Hypothesis test for proportion vs hypothesized value

Observed Hypothesized

0.7739 0.8 p (as decimal)

178/230 184/230 p (as fraction)

178. 184. X

230 230 n

0.0264 std. error

-0.99 z

.8387 p-value (one-tailed, upper)

Answers:

1: State the null & alternative hypothesis:

2: Identify the critical value

3: Identify the test statistic

4: State and explain your decision on H0