Exam 10: Hypothesis Tests Regarding a Parameter

Test Hypotheses about a Population Proportion - $\text { Test the claim that } \sigma ^ { 2 } < 44.8 \text { if } \mathrm { n } = 28 \text {, } \mathrm { s } ^ { 2 } = 28 \text {, and } \alpha = 0.10 \text {. Assume that the population is normally distributed. }$

(Short Answer)

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Question 141

Test Hypotheses about a Population Proportion -Test the claim that $\sigma ^ { 2 } \leq 28.8$ if $\mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 55.8$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

(Short Answer)

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Question 142

Provide an appropriate response. -A popular referendum on the ballot is favored by more than half of the voters. Write the null and alternative hypotheses.

(Short Answer)

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Question 143

Provide an appropriate response. -The mean annual return for an employee s IRA is at most 3.1 percent. Write the null and alternative hypotheses.

(Short Answer)

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Question 144

Test Hypotheses about a Population Mean with Known Using the Classical Approach -A local judge claims that the mean prison time for car thieves is less than the required 4 years. A sample of 80 convicted car thieves was randomly selected, and the mean length of prison time was found to be 3 years and 6 months, with a standard deviation of 1 year and 3 months. At $\alpha = 0.05$ , test the judge's claim.

(Short Answer)

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Question 145

Test Hypotheses about a Population Proportion -Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than $85 \%$ of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 330 manufacturing firms is selected, and only 28 of them offer child-care benefits. Specify the rejection region that the union will use when testing at $\alpha = 0.10$ .

(Essay)

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Question 146

Test Hypotheses about a Population Proportion -Test the claim that $\sigma \neq 13.05$ if $\mathrm { n } = 10 , \mathrm {~s} = 13.7$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

(Short Answer)

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Question 147

Test Hypotheses about a Population Proportion -According to a local chamber of commerce, in 1993, $5.9 \%$ of local area residents owned more than five cars. A local car dealer claims that the percentage has increased. He randomly selects 180 local area residents and finds that 12 of them own more than five cars. Test this car dealer's claim at the $\alpha = 0.05$ level of significance.

(Short Answer)

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Question 148

Explain the Logic of Hypothesis Testing -Find the critical value for a left-tailed test with $\alpha = 0.025$ .

(Multiple Choice)

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Question 149

Test Hypotheses about a Population Proportion -In $2000,36 \%$ of adults in a certain country were morbidly obese. A health practitioner suspects that the percent has changed since then. She obtains a random sample of 1042 adults and finds that 393 are morbidly obese. Is this sufficient evidence to support the practitioner's claim at the $\alpha = 0.1$ level of significance?

(Short Answer)

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Question 150

Test Hypotheses about a Population Proportion -A power curve is a graphic that plots

(Multiple Choice)

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Question 151

State Conclusions to Hypothesis Tests -The mean number of rushing yards for one NFL team was less than 95 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

(Multiple Choice)

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Question 152

Test Hypotheses about a Population Proportion -The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from $30 \%$ , then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is $2.5$ . Find the $\mathrm { P }$ -value for a two-tailed test of hypothesis.

(Multiple Choice)

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Question 153

Test Hypotheses about a Population Proportion -The engineering school at a major university claims that $20 \%$ of its graduates are women. In a graduating class of 210 students, 58 were females. Does this suggest that the school is believable? Use $\alpha = 0.05$ .

(Short Answer)

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Question 154

Test Hypotheses about a Population Proportion -Listed below are the April utility bills (in dollars) for one neighborhood. Assuming that the data is normally distributed, test the claim that the standard deviation for the data is $\$ 15$ . Use $\alpha = 0.01$ . 70 48 41 68 69 55 70 57 60 83 32 60 72 58

(Short Answer)

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Question 155

State Conclusions to Hypothesis Tests -The dean of a major university claims that the mean number of hours students study at her University (per day ) is at most $5.5$ hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

(Multiple Choice)

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Question 156

Test Hypotheses about a Population Proportion - $\text { Test the claim that } \sigma ^ { 2 } < 44.8 \text { if } \mathrm { n } = 28 \text {, } \mathrm { s } ^ { 2 } = 28 \text {, and } \alpha = 0.10 \text {. Assume that the population is normally distributed. }$

Test Hypotheses about a Population Proportion -Test the claim that $\sigma ^ { 2 } \leq 28.8$ if $\mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 55.8$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

Provide an appropriate response. -A popular referendum on the ballot is favored by more than half of the voters. Write the null and alternative hypotheses.

Provide an appropriate response. -The mean annual return for an employee s IRA is at most 3.1 percent. Write the null and alternative hypotheses.

Test Hypotheses about a Population Proportion -Test the claim that $\sigma \neq 13.05$ if $\mathrm { n } = 10 , \mathrm {~s} = 13.7$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

Explain the Logic of Hypothesis Testing -Find the critical value for a left-tailed test with $\alpha = 0.025$ .

Test Hypotheses about a Population Proportion -A power curve is a graphic that plots

State Conclusions to Hypothesis Tests -The mean number of rushing yards for one NFL team was less than 95 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Test Hypotheses about a Population Proportion -The engineering school at a major university claims that $20 \%$ of its graduates are women. In a graduating class of 210 students, 58 were females. Does this suggest that the school is believable? Use $\alpha = 0.05$ .

State Conclusions to Hypothesis Tests -The dean of a major university claims that the mean number of hours students study at her University (per day ) is at most $5.5$ hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 10: Hypothesis Tests Regarding a Parameter

Test Hypotheses about a Population Proportion -Test the claim that σ2≤28.8\sigma ^ { 2 } \leq 28.8σ2≤28.8 if n=20, s2=55.8\mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 55.8n=20, s2=55.8 , and α=0.01\alpha = 0.01α=0.01 . Assume that the population is normally distributed.

Provide an appropriate response. -A popular referendum on the ballot is favored by more than half of the voters. Write the null and alternative hypotheses.

Provide an appropriate response. -The mean annual return for an employee s IRA is at most 3.1 percent. Write the null and alternative hypotheses.

Test Hypotheses about a Population Proportion -Test the claim that σ≠13.05\sigma \neq 13.05σ=13.05 if n=10, s=13.7\mathrm { n } = 10 , \mathrm {~s} = 13.7n=10, s=13.7 , and α=0.01\alpha = 0.01α=0.01 . Assume that the population is normally distributed.

Explain the Logic of Hypothesis Testing -Find the critical value for a left-tailed test with α=0.025\alpha = 0.025α=0.025 .

Test Hypotheses about a Population Proportion -A power curve is a graphic that plots

State Conclusions to Hypothesis Tests -The mean number of rushing yards for one NFL team was less than 95 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Test Hypotheses about a Population Proportion -The engineering school at a major university claims that 20%20 \%20% of its graduates are women. In a graduating class of 210 students, 58 were females. Does this suggest that the school is believable? Use α=0.05\alpha = 0.05α=0.05 .

State Conclusions to Hypothesis Tests -The dean of a major university claims that the mean number of hours students study at her University (per day ) is at most 5.55.55.5 hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Test Hypotheses about a Population Proportion -Test the claim that $\sigma ^ { 2 } \leq 28.8$ if $\mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 55.8$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

Test Hypotheses about a Population Proportion -Test the claim that $\sigma \neq 13.05$ if $\mathrm { n } = 10 , \mathrm {~s} = 13.7$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

Explain the Logic of Hypothesis Testing -Find the critical value for a left-tailed test with $\alpha = 0.025$ .

Test Hypotheses about a Population Proportion -The engineering school at a major university claims that $20 \%$ of its graduates are women. In a graduating class of 210 students, 58 were females. Does this suggest that the school is believable? Use $\alpha = 0.05$ .

State Conclusions to Hypothesis Tests -The dean of a major university claims that the mean number of hours students study at her University (per day ) is at most $5.5$ hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?