AP Stats Chapter 12 Multiple Choice Practice

You have surveyed people about the average amount of time (in hours) they watch TV and have the following hypothesis H_o:μ=2 and H_a: μ≠2 at an α=5% level. If you create a 95% confidence interval that is (2.2, 3.4), which of the following is the correct interpretation?

• Fail to reject the null

• Reject the null

• Accept the null

• decision can not be made with the following information

When making an inference about a population mean, which of the following suggests use of z-scores rather than t-scores?

• Outliers are absent

• The population is normal

• The sample size is under 30

• Strong skew is absent

• The population standard deviation is known

What i the probability of Type II error when a hypothesis test is being conducted at a 5 percent significance level?

• .05

• .1

• .9

• .95

• There is insufficient information to answer this question

Which of the following statements is incorrect?

• The significance level of a test is probability of a Type II error

• Given a particular alternative, the power of a test against the alternative is 1 minus the probability of a Type II error associated with that alternative.

• If the significance level remains fixed, increasing the sample size will reduce the probability of a Type II Error.

• If the significance level remains fixed, increasing the sample size will raise power

• Holding the sample size fixed, increasing the significance level will decrease the probability of a Type II error.

If all other variables remain constant, which of the following will not increase the power of a hypothesis test?

• Increasing sample size

• Increasing the significance level

• Increasing the probability of a Type II error

• Decreased variability in the data

• Increased distance betweeen the true and the hypothesized parameter

Given that the power of a significance test against a particular alternative is 96 percent, which of the following is true?

• The probability of mistakenly rejecting a true null hypothesis is less than 4%

• The probability of mistakenly rejecting a true null hypothesis is 4%

• The probability of mistakenly rejecting a true null hypothesis is greater than 4%

• The probability of mistakenly failing to reject a false null hypothesis is 4%

• The probability of mistakenly failing to reject a false null hypothesis is different than 4%

A company will market a new hybrid luxury car only if they can sell it for more than $50,000 (otherwise it will lose money). They do a random survey of 50 potential customers and run a hypothesis test with H_o: μ=50,000 and H_a:μ>50,000. What would be the consequences of Type I and Type II errors?

• Type I: produce a nonprofitable car; Type II: fail to produce a profitable car

• Type I: fail to produce a profitable car; Type II: fail to produce a nonprofitable car

• Type I: fail to produce a nonprofitable car; Type II: produce a profitable car

• Type I: fail to produce a profitable car; Type II: produce a profitable car

• Type I: produce a nonprofitable car; Type II: fail to produce a nonprofitable car

Which of the following is incorrect?

• The power of a test concerns its ability to detect a true alternative hypothesis.

• The significance level of a test is the probability of rejecting a true null hypothesis.

• The probability of a type I error plus the probability of a Type II error always equals 1.

• Power equals 1 minus the probability of failing to reject a false null hypothesis.

• Anything that makes a null hypothesis harder to reject will increase the probability of committing a Type II error.

In testing the null hypothesis H_o:μ = 75 against the alternative hypothesis H_a:μ>75, a sample from a normal population has a mean of 76.9 with a z-score of 2.23 and a p-value of 0.0175. Which of the following is not a reasonable conclusion?

• If the null hypothesis is assumed to be true, the probability of obtaining a sample mean as extreme a or more extreme than 76.9 is only 0.0175.

• In all samples using the same sample size and the sampling techniques, the null hypothesis will be wrong 1.75% of the time

• At a significance level of 5%, there is sufficient evidence to reject the null hypothesis.

• If the alternative hypothesis had been two-sided, then the same z-score would have resulted in a p-value of 2x0.0175

A manufacturer of heart lung machines periodically checks a sample of its products and performs a major re-calibration if readings are sufficiently off target. Similarly, a rug manufacturer periodically checks the sizes of its throw rugs coming off the assembly line and halts production if measurements are sufficiently off target. In both situations, we have the null hypothesis that the production equipment is performing satisfactorily. For each situation, which is more serious, a Type I or Type II?

• Machine Producer: Type I error, Carpet manufacturer: Type I error

• Machine Producer: Type I error, Carpet manufacturer: Type II error

• Machine Producer: Type II error, Carpet manufacturer: Type I error

• Machine Producer: Type II error, Carpet manufacturer: Type II error

• This is impossible to answer without making an expected value judgement between human life and accurate throw rug sizes.