# Chapter 19-22

10 Questions | Total Attempts: 292

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• 1.
A manufacturer wishes to estimate the proportion of washing machines leaving the factory that is defective. How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.2%?
• A.

4,704

• B.

9,393

• C.

6,670

• D.

11,512

• E.

Not enough information

• 2.
A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school.  Find the margin of error for this poll if we want to have 99% confidence in our estimate of the percent of residents in favor of this proposed referendum.
• A.

5.53%

• B.

1%

• C.

0.5%

• D.

11.06%

• E.

4.86%

• 3.
A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a P-value of 0.075. What is reasonable to conclude about the new programs?
• A.

We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. There is no evidence the new programs are more effective, but we cannot conclude the new programs have no effect on retention.

• B.

There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective.

• C.

We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective.

• D.

There is a 7.5% chance of the new programs having no effect on retention.

• E.

There is a 92.5% chance of the new programs having no effect on retention.

• 4.
We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the value of z* to a smaller number. II. take a larger sample. III. take a smaller sample.
• A.

II only

• B.

III only

• C.

I and III

• D.

I only

• E.

I and II

• 5.
Write the null and alternative hypothesis you would use to test the following situation.  At a local university, only 62% of the original freshman class graduated in four years. Has this percentage changed?
• A.

Ho: p = 0.62 Ha: p ≠ 0.62

• B.

Ho: p ≠ 0.62 Ha: p = 0.62

• C.

Ho: p = 0.62 Ha: p < 0.62

• D.

Ho: p < 0.62 Ha: p > 0.62

• E.

Ho: p < 0.62 Ha: p = 0.62

• 6.
A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate. Identify the Type I error in this context.
• A.

The university concludes that retention is on the rise, but in fact the new programs do not help retention.

• B.

The product of the university's sample size and sample proportion was less than 10.

• C.

The university sampled all students at the university.

• D.

The university concludes that retention is on the rise since the retention rate can only increase.

• E.

The university stops all new programs, but in fact retention is on the rise and the programs help.

• 7.
Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (Ho: p = 0.97 and Ha: p > 0.97). The test results in a P-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?
• A.

They fail to reject Ho, making a Type II error.

• B.

They fail to reject Ho , making a Type I error.

• C.

They reject Ho , making a Type I error.

• D.

They correctly fail to reject Ho.

• E.

They correctly reject Ho.

• 8.
The mayor of a large city will run for govenor if he believes that more than 30 percent of the voters in the state already support him.  He will have a survey firm ask a random sample of n voters whether or not they support him.  He will use a large sample test for proportions to test the null hypothesis that the proportion of all voters who support him is 30 percent. Suppose that 35 percent of all voters in the state actually support him.  In which of the following situations would the power of this test be highest?
• A.

The mayor uses a significance level of 0.05 and n = 1,000 voters.

• B.

The mayor uses a significance level of 0.01 and n = 250 voters.

• C.

The mayor uses a significance level of 0.01 and n = 500 voters.

• D.

The mayor uses a significance level of 0.01 and n = 1,000 voters.

• E.

The mayor uses a significance level of 0.05 and n = 500 voters.

• 9.
When 252 college students are randomly selected and surveyed, it is found that 115 own a car. Construct a 99% confidence interval for the percentage of all college students who own a car.
• A.

(40.5%, 50.8%)

• B.

(37.6%, 53.7%)

• C.

(38.3%, 52.9%)

• D.

(25.3%, 66.0%)

• E.

(39.5%, 51.8%)

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