chapter 7
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.
