Section 1 Homework

A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. *H₀*: *σ ≥ 7.9* *H*∨*a*: *σ < 7.9* What type of test is being conducted in this​ problem? A.) Left​-tailed test B.) Right​-tailed test C.) Two​-tailed test

Correct Answer: A.) Left​-tailed test

What are the two decisions that you can make from performing a hypothesis test? What are the two decisions that you can make from performing a hypothesis test? Select all that apply. A.) make a type I error B.) accept the alternative hypothesis C.) accept the null hypothesis D.) fail to reject the null hypothesis E.) reject the alternative hypothesis F.) make a type II error G.) fail to reject the alternative hypothesis H.) reject the null hypothesis

Correct Answer(s): D.) fail to reject the null hypothesis H.) reject the null hypothesis

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.* Choose the correct answer below. A.) False. In a hypothesis test, you make no assumptions. B.) False. In a hypothesis test, you assume the null hypothesis is true. C.) True.

Correct Answer: B.) False. In a hypothesis test, you assume the null hypothesis is true.

The three confidence intervals to the right (below) represent three samplings. Decide whether each confidence interval indicates that you should reject *H₀*. Explain your reasoning. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) *(Original):* An infinite number line, labeled from 74 to 80, has tick marks in increments of 1. The region to the right of a closed circle at 77 is shaded and labeled *"H₀": μ ≥ 77*. *(A):* An infinite number line, labeled from 74 to 80, has tick marks in increments of 1. The region between an open circle at 75 and an open circle at 76 is shaded and labeled *75 < μ < 76*. *(B):* An infinite number line, labeled from 74 to 80, has tick marks in increments of 1. The region between an open circle at 78 and an open circle at 79 is shaded and labeled *78 < μ < 79*. *(C):* An infinite number line, labeled from 74 to 80, has tick marks in increments of 1. The region between an open circle at 74.5 and an open circle at 79.5 is shaded and labeled *74.5 < μ < 79.5*. *Part 1 (a):* Choose the correct answer below. A.) Reject *H₀*. The confidence interval includes values greater than 77. B.) Fail to reject *H₀*. The confidence interval includes values greater than 77. C.) Reject *H₀*. The confidence interval is located to the left of 77. D.) Fail to reject *H₀*. The confidence interval is located to the left of 77. *Part 2 (b):* Choose the correct answer below. A.) Reject *H₀*. The confidence interval includes values less than 77. B.) Reject *H₀*. The confidence interval includes values greater than 77. C.) Fail to reject *H₀*. The confidence interval includes values less than 77. D.) Fail to reject *H₀*. The confidence interval includes values greater than 77. *Part 3 (c):* Choose the correct answer below. A.) Fail to reject *H₀*. The confidence interval includes values greater than 77. B.) Fail to reject *H₀*. The confidence interval includes values less than 77. C.) Reject *H₀*. The confidence interval includes values greater than 77. D.) Reject *H₀*. The confidence interval includes values less than 77.

Correct Answers: *Part 1 (a):* C.) Reject *H₀*. The confidence interval is located to the left of 77. *Part 2 (b):* D.) Fail to reject *H₀*. The confidence interval includes values greater than 77. *Part 3 (c):* A.) Fail to reject *H₀*. The confidence interval includes values greater than 77.

The three confidence intervals to the right (below) represent three samplings. Decide whether each confidence interval indicates that you should reject *H₀*. Explain your reasoning. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) *(Original):* An infinite number line, labeled from 0.22 to 0.28, has tick marks in increments of 1. The region to the left of a closed circle at 0.25 is shaded and labeled *"H₀": p ≤ 0.25*. *(A):* An infinite number line, labeled from 0.22 to 0.28, has tick marks in increments of 1. The region between an open circle at 0.26 and an open circle at 0.27 is shaded and labeled *0.26 < p < 0.27*. *(B):* An infinite number line, labeled from 0.22 to 0.28, has tick marks in increments of 1. The region between an open circle at 0.24 and an open circle at 0.26 is shaded and labeled *0.24 < p < 0.26*. *(C):* An infinite number line, labeled from 0.22 to 0.28, has tick marks in increments of 1. The region between an open circle at 0.225 and an open circle at 0.235 is shaded and labeled *0.225 < p < 0.235*. *Part 1 (a):* Choose the correct answer below. A.) Fail to reject *H₀*. The confidence interval is located to the right of 0.25. B.) Reject *H₀*. The confidence interval includes values less than 0.25. C.) Reject *H₀*. The confidence interval is located to the right of 0.25. D.) Fail to reject *H₀*. The confidence interval includes values less than 0.25. *Part 2 (b):* Choose the correct answer below. A.) Fail to reject *H₀*. The confidence interval includes values less than 0.25. B.) Reject *H₀*. The confidence interval includes values greater than 0.25. C.) Reject *H₀*. The confidence interval includes values less than 0.25. D.) Fail to reject *H₀*. The confidence interval includes values greater than 0.25. *Part 3 (c):* Choose the correct answer below. A.) Reject *H₀*. The confidence interval includes values less than 0.25. B.) Fail to reject *H₀*. The confidence interval includes values less than 0.25. C.) Reject *H₀*. The confidence interval includes values greater than 0.25. D.) Fail to reject *H₀*. The confidence interval includes values greater than 0.25.

Correct Answers: *Part 1 (a):* C.) Reject *H₀*. The confidence interval is located to the right of 0.25. *Part 2 (b):* A.) Fail to reject *H₀*. The confidence interval includes values less than 0.25. *Part 3 (c):* B.) Fail to reject *H₀*. The confidence interval includes values less than 0.25.

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 report claims that less than 75% of households in a specific county struggle to afford basic necessities.* *Part 1:* Does the claim represent the null hypothesis or the alternative​ hypothesis? Since the claim *_______(1)_______* a statement of​ equality, it represents the *_____(2)_____* hypothesis. *Part 2 (a):* How should you interpret a decision that rejects the null​ hypothesis? There *_(1)_* enough evidence to *____(2)____* the claim that less than 75% of households in a county struggle to afford basic necessities. *Part 3 (b):* How should you interpret a decision that fails to reject the null​ hypothesis? There *___(1)___* evidence to *____(2)____* the claim that less than 75% of households in a county struggle to afford basic necessities.

Correct Answers: *Part 1:* *(1):* *does not contain* *(2):* *alternative* *Part 2 (a):* *(1):* *is* *(2):* *support* *Part 3 (b):* *(1):* *is not* *(2):* *support*

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 less than 2.9 years.* *Part 1:* Does the claim represent the null hypothesis or the alternative​ hypothesis? Since the claim *_______(1)_______* a statement of​ equality, it represents the *_____(2)_____* hypothesis. *Part 2 (a):* How should you interpret a decision that rejects the null​ hypothesis? There is *____(1)____* evidence to *____(2)____* the claim that the standard deviation of the life of a certain type of lawn mower is less than 2.9 years. *Part 3 (b):* How should you interpret a decision that fails to reject the null​ hypothesis? There is *_____(1)_____* evidence to *____(2)____* the claim that the standard deviation of the life of a certain type of lawn mower is less than 2.9 years.

Correct Answers: *Part 1:* *(1):* *does not contain* *(2):* *alternative* *Part 2 (a):* *(1):* *sufficient* *(2):* *support* *Part 3 (b):* *(1):* *insufficient* *(2):* *support*

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 57 days.* *Part 1:* Does the claim represent the null hypothesis or the alternative​ hypothesis? Since the claim *_______(1)_______* a statement of​ equality, it represents the *_____(2)_____* hypothesis. *Part 2 (a):* How should you interpret a decision that rejects the null​ hypothesis? There is *____(1)____* evidence to *____(2)____* the claim that the mean incubation period for the eggs of a species of bird is more than 57 days. *Part 3 (b):* How should you interpret a decision that fails to reject the null​ hypothesis? There is *_____(1)_____* evidence to *____(2)____* the claim that the mean incubation period for the eggs of a species of bird is more than 57 days.

Correct Answers: *Part 1:* *(1):* *does not contain* *(2):* *alternative* *Part 2 (a):* *(1):* *sufficient* *(2):* *support* *Part 3 (b):* *(1):* *insufficient* *(2):* *support*

A local chess club claims that the length of time to play a game has a standard deviation of 15 minutes or less. Write sentences describing type I and type II errors for a hypothesis test of this claim. *Part 1:* A type I error will occur if the actual standard deviation of the length of time to play a game is *__________(1)__________* 15 ​minutes, but you *___(2)___* the null​ hypothesis, *_____(3)_____*. *Part 2:* A type II error will occur if the actual standard deviation of the length of time to play a game is *________(1)________* 15 ​minutes, but you *_______(2)_______* the null​ hypothesis, *_____(3)_____*.

Correct Answers: *Part 1:* *(1):* *less than or equal to* *(2):* *reject* *(3):* *"H₀": σ ≤ 15* *Part 2:* *(1):* *greater than* *(2):* *fail to reject* *(3):* *"H₀": σ ≤ 15*

Use the given statement to represent a claim. Write its complement and state which is *H₀* and which is *H*∨*a*. *μ ≥ 556* *Part 1:* Find the complement of the claim. μ *_* 556 *Part 2:* Which is *H₀* and which is *H*∨*a*? A.) *H₀*: μ ≥ 556 *H*∨*a*: μ ≤ 556 B.) *H₀*: μ > 556 *H*∨*a*: μ ≥ 556 C.) *H₀*: μ ≤ 556 *H*∨*a*: μ ≥ 556 D.) *H₀*: μ ≥ 556 *H*∨*a*: μ < 556 E.) *H₀*: μ ≥ 556 *H*∨*a*: μ = 556 F.) *H₀*: μ = 556 *H*∨*a*: μ ≥ 556 G.) *H₀*: μ ≥ 556 *H*∨*a*: μ > 556 H.) *H₀*: μ < 556 *H*∨*a*: μ ≥ 556 I.) *H₀*: μ ≥ 556 *H*∨*a*: μ ≠ 556

Correct Answers: *Part 1:* *<* *Part 2:* D.) *H₀*: μ ≥ 556 *H*∨*a*: μ < 556

Use the given statement to represent a claim. Write its complement and state which is *H₀* and which is *H*∨*a*. *σ ≠ 13* *Part 1:* Find the complement of the claim. σ *_* 13 *Part 2:* Which is *H₀* and which is *H*∨*a*? A.) *H₀*: σ ≠ 13 *H*∨*a*: σ < 13 B.) *H₀*: σ = 13 *H*∨*a*: σ ≠ 13 C.) *H₀*: σ ≤ 13 *H*∨*a*: σ ≠ 13 D.) *H₀*: σ ≠ 13 *H*∨*a*: σ ≥ 13 E.) *H₀*: σ < 13 *H*∨*a*: σ ≠ 13 F.) *H₀*: σ ≠ 13 *H*∨*a*: σ ≤ 13 G.) *H₀*: σ ≥ 13 *H*∨*a*: σ ≠ 13 H.) *H₀*: σ ≠ 13 *H*∨*a*: σ > 13 I.) *H₀*: σ ≠ 13 *H*∨*a*: σ = 13

Correct Answers: *Part 1:* *=* *Part 2:* B.) *H₀*: σ = 13 *H*∨*a*: σ ≠ 13

Use the given statement to represent a claim. Write its complement and state which is *H₀* and which is *H*∨*a*. *p > 0.56* *Part 1:* Find the complement of the claim. p *_* 0.56 *Part 2:* Which is *H₀* and which is *H*∨*a*? A.) *H₀*: p < 0.56 *H*∨*a*: p > 0.56 B.) *H₀*: p > 0.56 *H*∨*a*: p ≥ 0.56 C.) *H₀*: p ≠ 0.56 *H*∨*a*: p > 0.56 D.) *H₀*: p ≤ 0.56 *H*∨*a*: p > 0.56 E.) *H₀*: p > 0.56 *H*∨*a*: p ≠ 0.56 F.) *H₀*: p > 0.56 *H*∨*a*: p ≤ 0.56 G.) *H₀*: p ≥ 0.56 *H*∨*a*: p > 0.56 H.) *H₀*: p > 0.56 *H*∨*a*: p > 0.56 I.) *H₀*: p > 0.56 *H*∨*a*: p < 0.56

Correct Answers: *Part 1:* *≤* *Part 2:* D.) *H₀*: p ≤ 0.56 *H*∨*a*: p > 0.56

Match the alternative hypothesis shown below with its graph to the right (below). Then state the null hypothesis and sketch its graph. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) *H*∨*a*: *σ ≠ 2* *(A):* An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the right of an open circle at 2 is shaded. *(B):* An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 2 is shaded. *(C):* An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of an open circle at 2 is shaded. *Part 1:* Match the alternative hypothesis to its graph. Choose the correct graph below. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) A.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 2 is shaded. B.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the right of an open circle at 2 is shaded. C.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of an open circle at 2 is shaded. *Part 2:* State the null hypothesis. *H₀*: σ *_* 2 *Part 3:* Sketch a graph of the null hypothesis. Choose the correct graph below. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) A.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. A labeled point is plotted at 2. B.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the right of a closed circle at 2 is shaded. C.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of and to the right of a closed circle at 2 is shaded. D.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of a closed circle at 2 is shaded.

Correct Answers: *Part 1:* A.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 2 is shaded. *Part 2:* *=* *Part 3:* A.) An infinite number line, labeled from 1 to 4, has tick marks in increments of 1. A labeled point is plotted at 2.

Describe type I and type II errors for a hypothesis test of the indicated claim. *A lumber store claims that no more than 75​% of its new customers will return to buy their next order of lumber.* *Part 1:* Describe the type I error. Choose the correct answer below. A.) A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber is at least 0.75, but you reject *H₀*: p ≥ 0.75. B.) A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber is no more than 0.75, but you reject *H₀*: p ≤ 0.75. C.) A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber is at least 0.75, but you fail to reject *H₀*: p ≥ 0.75. D.) A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber is no more than 0.75, but you fail to reject *H₀*: p ≤ 0.75. *Part 2:* Describe the type II error. Choose the correct answer below. A.) A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber is more than 0.75, but you fail to reject *H₀*: p ≤ 0.75. B.) A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber is less than 0.75, but you fail to reject *H₀*: p ≤ 0.75. C.) A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber is less than 0.75, but you reject *H₀*: p ≥ 0.75. D.) A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber is more than 0.75, but you reject *H₀*: p ≥ 0.75.

Correct Answers: *Part 1:* B.) A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber is no more than 0.75, but you reject *H₀*: p ≤ 0.75. *Part 2:* A.) A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber is more than 0.75, but you fail to reject *H₀*: p ≤ 0.75.

Match the alternative hypothesis shown below with its graph to the right (below). Then state the null hypothesis and sketch its graph. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) *H*∨*a*: *σ² > 8* *(A):* An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 8 is shaded. *(B):* An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of an open circle at 8 is shaded. *(C):* An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the right of an open circle at 8 is shaded. *Part 1:* Match the alternative hypothesis to its graph. Choose the correct graph below. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) A.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 8 is shaded. B.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the right of an open circle at 8 is shaded. C.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of an open circle at 8 is shaded. *Part 2:* State the null hypothesis. *H₀*: σ² *_* 8 *Part 3:* Sketch a graph of the null hypothesis. Choose the correct graph below. (Since I don't have Quizlet+, I can't insert the images of the actual infinite number lines; ergo, I pasted their descriptions.) A.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of a closed circle at 8 is shaded. B.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of and to the right of a closed circle at 8 is shaded. C.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of an open circle at 8 is shaded. D.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the right of a closed circle at 8 is shaded. E.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of and to the right of an open circle at 8 is shaded. F.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the right of an open circle at 8 is shaded.

Correct Answers: *Part 1:* B.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the right of an open circle at 8 is shaded. *Part 2:* *≤* *Part 3:* A.) An infinite number line, labeled from 7 to 10, has tick marks in increments of 1. The region to the left of a closed circle at 8 is shaded.

Identify the type I error and the type II error for a hypothesis test of the indicated claim. *The percentage of adults who have a job is less than 88%.* *Part 1:* Identify the type I error. Choose the correct answer below. A.) Reject the null hypothesis that the percentage of adults who have a job is less than 88% when it is actually true. B.) Fail to reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually false. C.) Reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually true. D.) Fail to reject the null hypothesis that the percentage of adults who have a job is less than 88% when it is actually false. *Part 2:* Identify the type II error. Choose the correct answer below. A.) Fail to reject the null hypothesis that the percentage of adults who have a job is less than 88% when it is actually false. B.) Fail to reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually false. C.) Reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually true. D.) Reject the null hypothesis that the percentage of adults who have a job is less than 88% when it is actually true.

Correct Answers: *Part 1:* C.) Reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually true. *Part 2:* B.) Fail to reject the null hypothesis that the percentage of adults who have a job is greater than or equal to 88% when it is actually false.

What are the two types of hypotheses used in a hypothesis test? How are they related? *Part 1:* What are the two types of hypotheses used in a hypothesis test? A.) population and sample B.) left-tailed and right-tailed C.) type I and type II D.) null and alternative *Part 2:* How are they related? A.) They are equal. B.) They sum to zero. C.) One is a subset of the other. D.) They are complements.

Correct Answers: *Part 1:* D.) null and alternative *Part 2:* D.) They are complements.