chapter 7

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Explain the difference between the​ z-test for μ using rejection​ region(s) and the​ z-test for μ using a​ P-value.

in the​ z-test using rejection​ region(s), the test statistic is compared with critical values. The​ z-test using a​ P-value compares the​ P-value with the level of significance α.

Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. μ≥233 1. complement of the claim 2. Which is H0 and Ha

1. < 2. H0​: μ≥233 Ha​: μ<233

A local chess club claims that the length of time to play a game has a mean of less than 49 minutes. Write sentences describing type I and type II errors for a hypothesis test of this claim.

1. A type I error will occur if the actual mean of the length of time to play a game is greater than or equal to 49 ​minutes, but you reject the null​ hypothesis, H0: μ≥49 2. A type II error will occur if the actual mean of the length of time to play a game is less than 49 minutes, but you fail to reject the null​ hypothesis, H0: μ≥49 .

Describe type I and type II errors for a hypothesis test of the indicated claim. A shoe store claims that no more than 10​% of its new customers will return to buy their next pair of shoes. 1. type 1 error 2. type 2 error

1. A type I error will occur when the actual proportion of new customers who return to buy their next pair of shoes is no more than 0.10​,but you reject H0​: p≤0.10. 2. A type II error will occur when the actual proportion of new customers who return to buy their next pair of shoes is more than 0.10​,but you fail to reject H0​: p≤0.10.

Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of adults who retire at age 65 is less than 62%. 1. type 1 2. type 2

1. Reject the null hypothesis that the percentage of adults who retire at age 65 is greater than or equal to 62% when it is actually true. 2. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is greater than or equal to 62% when it is actually false.

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is​ performed, how should you interpret a decision that​ (a) rejects the null hypothesis or​ (b) fails to reject the null​ hypothesis? A researcher claims that the standard deviation of the life of a certain type of lawn mower is more than 2.5 years. 1. Does the claim represent the null hypothesis or the alternative​ hypothesis? ​(a) How should you interpret a decision that rejects the null​ hypothesis? ​(b) How should you interpret a decision that fails to reject the null​ hypothesis?

1. Since the claim does not contain a statement of​ equality, it represents the alternative hypothesis a. There is sufficient evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.5 years b. There is insufficient evidence to support the claim that the standard deviation of the life of a certain type of lawn mower is more than 2.5 years

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is​ performed, how should you interpret a decision that​ (a) rejects the null hypothesis or​ (b) fails to reject the null​ hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is more than 52 days. 1. Does the claim represent the null hypothesis or the alternative​ hypothesis? ​(a) How should you interpret a decision that rejects the null​ hypothesis? ​(b) How should you interpret a decision that fails to reject the null​ hypothesis?

1. Since the claim does not contain a statement of​ equality, it represents the alternative hypothesis. a. There is sufficient evidence to support the claim that the mean incubation period for the eggs of a species of bird is more than 52 days. b. There is insufficient evidence to support the claim that the mean incubation period for the eggs of a species of bird is more than 52 days.

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is​ performed, how should you interpret a decision that​ (a) rejects the null hypothesis or​ (b) fails to reject the null​ hypothesis? 1. Does the claim represent the null hypothesis or the alternative​ hypothesis? ​(a) How should you interpret a decision that rejects the null​ hypothesis? ​(b) How should you interpret a decision that fails to reject the null​ hypothesis?

1. Since the claim does not contain a statement of​ equality, it represents the alternative hypothesis. a. There is enough evidence to support the claim that less than 70​% of households in a county struggle to afford basic necessities. b. There is not enough evidence to support the claim that less than 70​% of households in a county struggle to afford basic necessities.

What are the two types of hypotheses used in a hypothesis​ test? How are they​ related? 1. What are the two types of hypotheses used in a hypothesis​ test? 2. How are they​ related?

1. null and alternative 2. They are complements.

Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. p<0.69 1. complement of claim 2. H0 and Ha

1. ≥ 2. H0​: p≥0.69 Ha​: p<0.69

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. In a hypothesis​ test, you assume the alternative hypothesis is true.

False. In a hypothesis​ test, you assume the null hypothesis is true.

Explain how to decide when a normal distribution can be used to approximate a binomial distribution.

If np≥5 and nq≥​5, the normal distribution can be used.

Explain how to find the critical values for a​ t-distribution. a. first step b. find critical values using the given t distribution table in the row w the correct degrees of freedom

a. Identify the level of significance α and the degrees of​ freedom, d.f.=n−1. b. If the hypothesis test is​ left-tailed, use the "One tail, α" column with a negative sign. If the hypothesis test is​ right-tailed, use the "One tail, α" column with a positive sign. If the hypothesis test is​ two-tailed, use the "Two tails comma alpha ""Two tails, α" column with a negative and a positive sign.

What are the two decisions that you can make from performing a hypothesis​ test?

a. reject the null hypothesis b. fail to reject the null hypothesis

In hypothesis​ testing, does choosing between the critical value method or the​ P-value method affect your​ conclusion? Explain.

​No, because both involve comparing the test​ statistic's probability with the level of significance.


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