# Hypothesis testing, confidence interval for mean and proportion

See the attached file.

1-

A snack food company produces bags of peanuts labeled as containing 4 ounces. A consumer reports organization wants to see if the weight is actually less than 4 ounces. They randomly choose 40 bags and their contents are weighed. They find the average weight is 3.5 ounces with a standard deviation of s = 0.9 ounces. Is this sufficient evidence to conclude that the bags contain less than 4 ounces of peanuts?

a. State the null and alternative hypotheses.

H0:

Ha:

b. What is the value of the one-sample t statistic? Do not pool variances.

t = Round to 3 places.

c. What is the P-value for the t test?

P-value = Round to 4 places.

d. Is there sufficient evidence that the bags contain less than 4 ounces of peanuts?

e. Give a 95% confidence interval for the mean weight of peanuts in each bag. (The t critical value is 2.009.)

From ounces to ounces. Round each number to 2 places.

2-

Simple random sample of high-interest mortgages and low-interest mortgages were obtained. For the 61 high-interest mortgages, the borrowers had a mean FICO credit score of 585 and a standard deviation of 51.5. For the 22 low interest mortgages, the borrowers had a mean FICO score of 636 and a standard deviation of 36.8. Test the claim that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

a. State the null and alternative hypotheses.

H0:

Ha:

b. What is the value of the two-sample t statistic? Do not pool variances.

t = Round to 3 places.

c. What is the P-value for the t test? Use degrees of freedom of 21 or technology.

P-value = Round to 4 places.

d. Does the FICO credit rating score appear to affect mortgage payments?

o There is sufficient evidence to show that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

o There is not sufficient evidence to show that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of borrowers with low-interest mortgages.

e. Give a 90% confidence interval for the mean difference between FICO scores of high-interest and low-interest borrowers. Answer using technology or if completed by hand use degrees of freedom of 52.05.

From a score of __ to a score of ____ . Round each number to 2 places.

3-

According to the National Institute on Alcohol Abuse and Alcoholism, 50% of college students nationwide engage in "binge drinking" behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is actually lower than the national proportion. In a commissioned study, 347 students are selected randomly from a list of all students enrolled at the college. Of these 156 admitted to having engaged in binge drinking.

a. What is the sample proportion?

Round to 4 places.

b. What is the standard error of the sample proportion?

Round to 4 places.

c. Give a 95% confidence interval for the true proportion of students who binge drink at her college.

From ____ to ______. Round to 2 places. Do not enter as a percent.

d. State the null and alternative hypotheses.

H0:

Ha:

e. Give the test statistic.

= Round to 3 places.

f. State the p-value for this test.

P-value = Round to 4 places.

g. Do the students at this college binge drink less than students do nationwide? (Significance level of α = 0.10.)

o Yes, because the P-value is less than the level of significance

o Yes, because the P-value is greater than the level of significance

o No, because the P-value is less than the level of significance

o No, because the P-value is greater than the level of significance

4-

The P-value for a test was P = 0.026.

a. Is this significant at the 5% level?

o Maybe

o Yes

o No

b. Is this significant at the 1% level?

o Maybe

o No

o Yes

5-

A significance test was reported in an article said the result was significant at the 1% level. Are such results always, sometimes, or never significant at the 5% level?

• Always.

• Sometimes.

• Never

6-

You wish to test the following claim ( ) at a significance level of .

You believe the population is normally distributed, but you do not know the standard deviation.

Data

74.4

87.8

70.5

79.5

66.1

79.7

94.4

69.6

85.0

76.4

85.3

85.9

81.5

69.1

61.4

92.5

77.1

71.8

78.0

101.6

89.6

81.8

68.5

80.3

98.5

82.9

101.6

98.5

99.4

77.7

88.5

72.6

65.3

95.6

85.9

70.5

76.7

82.1

76.1

101.6

92.9

99.4

85.0

77.1

66.1

Use StatCrunch.

• Copy and paste the data into an empty column in Statcrunch

• Select Stat → T Statistics → One Sample → From data

• Select the column the data is in

• Enter the appropriate null claim and alternative hypothesis.

• Press Compute!

a. What is the test statistic for this sample?

test statistic = Round to 3 decimal places

b. What is the p-value for this sample?

p-value = Use Technology Round to 4 decimal places.

c. The p-value is...

o less than (or equal to)

o greater than

d. This test statistic leads to a decision to...

o reject the null

o accept the null

o fail to reject the null

e. As such, the final conclusion is that...

o There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 78.4.

o There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 78.4.

o The sample data support the claim that the population mean is greater than 78.4.

o There is not sufficient sample evidence to support the claim that the population mean is greater than 78.4.

#### Solution Preview

See attached for solution.

1-

A snack food company produces bags of peanuts labeled as containing 4 ounces. A consumer reports organization wants to see if the weight is actually less than 4 ounces. They randomly choose 40 bags and their contents are weighed. They find the average weight is 3.5 ounces with a standard deviation of s = 0.9 ounces. Is this sufficient evidence to conclude that the bags contain less than 4 ounces of peanuts?

a. State the null and alternative hypotheses.

H0:

Ha:

b. What is the value of the one-sample t statistic? Do not pool variances.

t = Round to 3 places.

c. What is the P-value for the t test?

P-value = Round to 4 places.

d. Is there sufficient evidence that the bags contain less than 4 ounces of peanuts?

Yes, there is a sufficient evidence that the bags contain less than 4 ounces of peanuts.

e. Give a 95% confidence interval for the mean weight of peanuts in each bag. (The t critical value is 2.009.)

From ounces to ounces. Round each number to 2 places.

2-

Simple random sample of high-interest mortgages and low-interest mortgages were obtained. For the 61 high-interest mortgages, the borrowers had a mean FICO credit score of 585 and a standard deviation of 51.5. For the 22 low interest mortgages, the borrowers had a mean FICO score of 636 and a standard deviation of 36.8. Test the claim that the mean FICO score of borrowers with high-interest mortgages is lower than the mean FICO score of ...

#### Solution Summary

This solution is comprised of a detailed explanation Z test for proportion of one sample, t test for mean for one sample and t test for mean for two samples. This solution mainly discussed the 6 questions in the attachments with the help of excel for calculations of test statistics etc. This solution explained the questions with interpretation of the output of Z test for proportion of one sample, t test for mean for one sample and t test for mean for two sample.