Stats 2 chapter 9

We use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required. T/F

True. We use the alternative hypothesis as a vehicle to establish something new, that is, to contest the status quo

A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error? A) 1% B) 5% C) 95% D) 99%

A) 1%

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A) Type I: 4%, Type II: 6% B) Type I: 6%, Type II: 4% C) Type I: 94%, Type II: 4% D) Type I: 4%, Type II: 94%

A. Type I: 4%, Type II: 6%

The hypothesis statement H: μ < 60 is an example of a(an) ________ hypothesis.

Alternative hypothesis. Null uses the following signs: =, ≥, ≤; the alternative hypothesis is then specified with the corresponding opposite sign: ≠, >, <.

We define the allowed probability of making a Type I error as α, and we refer to 100α% as the ________.

Significance level

Given the ________ of the z distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

Symmetry

A Type I error is committed when we reject the null hypothesis, which is actually true. T/F

TRUE. A Type I error is committed when we reject the null hypothesis, which is actually true.

The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis.

null hypothesis. Null uses the following signs: =, ≥, ≤; the alternative hypothesis is then specified with the corresponding opposite sign: ≠, >, <.

If we reject a null hypothesis at the 1% significance level, then we have ________ evidence that the null hypothesis is false.

Very strong. If we reject a null hypothesis at the 1% significance level (α = 0.01), then we have very strong evidence that the null hypothesis is false.

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are ________. A) H0: p ≤ 0.065, HA: p > 0.065 B) H0: ≥ 0.065, HA: < 0.065 C) H0: p = 0.081, HA: p ≠ 0.081 D) H0: p ≥ 0.081, HA: p < 0.081

D. The competing hypotheses are H0: p ≥ p0, HA: p < p0. It is referred to as a left-tailed test of the population proportion.

The alternative hypothesis typically agrees with the status quo. T/F

False. The alternative hypothesis contradicts the default state of nature or status quo.

On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis." T/F

False. We either "reject the null hypothesis" or "do not reject the null hypothesis."

A recent report claimed that Americans are retiring later in life. An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 = 1.92. With α = 0.05, she ________. A) rejects the null hypothesis and concludes that the mean retirement age has increased B) rejects the null hypothesis and concludes that the mean retirement age has not increased C) does not reject the null hypothesis and does not conclude that the mean retirement age has changed D) does not reject the null hypothesis and does not conclude that the mean retirement age has increased

A. For a right-tailed test, the p-value is computed as P(T ≥ t). The decision rule is to reject the null hypothesis if the p-value < α and not reject the null hypothesis if the p-value ≥ α.

21) A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H0: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that ________. A) the franchiser builds on an acceptable site B) the franchiser builds on an unacceptable site C) the franchiser does not build on an acceptable site D) the franchiser does not build on an unacceptable site

B. A Type I error is committed when we reject the null hypothesis when the null hypothesis is actually true.

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H0: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that ________. A) the franchiser builds on an acceptable site B) the franchiser builds on an unacceptable site C) the franchiser does not build on an acceptable site D) the franchiser does not build on an unacceptable site

C. A Type II error is made when we do not reject the null hypothesis and the null hypothesis and the null hypothesis is actually false.

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false. T/F

FALSE. A Type II error is made when we do not reject the null hypothesis that is actually false.

A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean X hat

TRUE. A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean X hat.

In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails. T/F

TRUE. A one-tailed test involves a null hypothesis that can be rejected only on one side of the hypothetical value. In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter

Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample.

TRUE. The p-value is the likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample, under the assumption that the null hypothesis is true as an equality.

For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.

True. By reducing Type I error, we implicitly increase Type II error, and vice versa.

The null hypothesis typically corresponds to a presumed default state of nature. T/F

True. We think of the null hypothesis as corresponding to a presumed default state of nature or status quo.

A(n) ________ error is committed when we reject the null hypothesis when the null hypothesis is true.

Type 1 error