Chapter 8-1

Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of adults who retire at age 65 is less than 62%. Identify the type I error. Choose the correct answer below. a) Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually equal to 62%. b) Fial to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when the percentage is actually less than 62%. c) Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62% when the percentage is actually equal to 62%. d) Reject the null hyphothesis that the percentage of adults who retire at age 65 is less than 62% when that percentage is actually less than 62%. Identify the type II error. Choose the correct answer below. a) Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62% when the percentage is actually equal to 62%. b) Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually less than 62%. c) Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62% when that percentage is actually less than 62%. d) Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when the percentage is actually equal to 62%.

Identify the type I error. Choose the correct answer below. a) Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually equal to 62%. Identify the type II error. Choose the correct answer below. b) Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually less than 62%.

A bottle contains a label stating that it contains pills with 500 mg of vitamin​ C, and another bottle contains a label stating that it contains pills with 325 mg of aspirin. When testing claims about the mean contents of the​ pills, which would have more serious​ implications: rejection of the vitamin C claim or rejection of the aspirin​ claim? Considering only a type I error and using the same sample​ size, is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of​ aspirin? Rejection of the claim about __________ is more serious because the wrong __________ dosage could cause more serious adverse reactions than a wrong __________ dosage. It would be wise to use a __________ significance level for testing the claim about the aspirin.

Rejection of the claim about _aspirin_ is more serious because the wrong _aspirin_ dosage could cause more serious adverse reactions than a wrong _vitamin C_ dosage. It would be wise to use a _smaller_ significance level for testing the claim about the aspirin.

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical​ trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p>​0.5, which corresponds to the claim that the method increases the likelihood of having a​ girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the​ method, which of the following​ P-values would you​ prefer: 0.999,​ 0.5, 0.95,​ 0.05, 0.01,​ 0.001? Why? The P-value of __________ is preferred because it corresponds to the sample evidence that most strongly supports the __________ hypothesis that the method __________ effective.

The P-value of _0.001_ is preferred because it corresponds to the sample evidence that most strongly supports the _alternative_ hypothesis that the method _is_ effective.

The __________ hypothesis is a statment that the value of a population parameter is equal to some claimed value.

The _null_ hypothesis is a statment that the value of a population parameter is equal to some claimed value.

The __________ is a value used in making a decision about the null hypothesis and is found by conversting the smaple statistic to a score with the assumption that the null hypothesis is true.

The _test statistic_ is a value used in making a decision about the null hypothesis and is found by conversting the smaple statistic to a score with the assumption that the null hypothesis is true.

Claim: The mean pluse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 167 adult males, the mean pulse rate is 68.8 bpm and the standrd deviation is 11.2. Find the value of the test statistic. The value of the test statistic is _____.

The value of the test statistic is _-0.23_. T-Test(69,68.8,11.2,167)= -0.23

Claim: Fewer than 90% of adults have a cell phone. In a reputable poll of 1041 adults, 81% said they have a cell phone. Find the value of the test statistic. The value of the test statistic is ______.

The value of the test statistic is _-9.70_. 0.81*1041=843 1-PropZTest(0.90,843,1041,<P0)= -9.70

Claim: The standard deviation of pulse rates of adult males is more than 11 bpm. For a random sample of 155 adult males, the pulse rates have a standard deviation of 11.4 bpm. Find the value of the test statistic. The value of the test statistic is _____.

The value of the test statistic is _165.40_. (155-1)/11^2= 1.272727273*11.4^2=165.40

Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 607 randomly selected adults showed that 61% of them would erase all of their personal information online if they could. Find the value of the test statistic. The value of the test statistic is _____.

The value of the test statistic is _____.

Idenfity the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.28. Which of the following is a type I error? a) Fail to reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually different from 0.28. b) Fail to reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually 0.28. c) Reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually 0.28. d) Reject the claim that the proportion of people who write with their left ahnd is 0.28 when the proportion is actually different from 0.28. Which of the following is a type II error? a) Fail to reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually 0.28. b) Fail to reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually different from 0.28. c) Reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually different from 0.28. d) Reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually 0.28.

Which of the following is a type I error? c) Reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually 0.28. Which of the following is a type II error? b) Fail to reject the claim that the proportion of people who write with their left hand is 0.28 when the proportion is actually different from 0.28.

Claim: The standard deviation of pulse rates of adult males is less than 11 bpm. For a random sample of 142 adult males, the pulse rates have a standard deviation of 10.2 bpm. Complete parts (a) and (b) below. a) Express the original claim in symbolic form. _____ _____ _____ bpm b) Identify the null and alternative hypotheses. H0: _____ _____ _____ bpm H1: _____ _____ _____ bpm

a) Express the original claim in symbolic form. _σ_ _<_ _11_ bpm b) Identify the null and alternative hypotheses. H0: _σ_ _=_ _11_ bpm H1: _σ_ _<_ _11_ bpm

Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69.5 bpm. For a random sample of 129 adult males, the mean pulse rate is 70.8 bpm and the standard deviation is 10.9 bpm. Complete parts (a) and (b) below. a) Express the original claim in symbolic form. _____ _____ _____ bpm b) Identify the null and alternative hypotheses. H0: _____ _____ _____ bpm H1: _____ _____ _____ bpm

a) Express the original claim in symbolic form. _μ_ _=_ _69.5_ bpm b) Identify the null and alternative hypotheses. H0: _μ_ _=_ _69.5_ bpm H1: _μ_ _≠_ _69.5_ bpm

Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 421 randomly selected adults showed that 55% of them would erase all of their personal information online if they could. Complete parts (a) and (b) below. a) Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information. _____ _____ _____ b) Identify the null and alternative hypotheses. H0​: _____ _____ _____ H1​: _____ _____ _____

a) Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information. _p_ _>_ _0.5_ b) Identify the null and alternative hypotheses. H0​: _p_ _=_ _0.5_ H1​: _p_ _>_ _0.5_

Assume a significance level of α=0.05 and use the given information to complete parts (a) and (b) below. Original claim: More than 52% of adults would erase all of their personal information online if they could. The hypothesis test results in P-value of 0.0087. a) State a conclusion about the null hypothesis (Reject H0 or fail to reject H0.) Choose the correct answer below. A) Fail to reject H0 because the P-value is less than or equal to α. B) Reject H0 because the P-value is greater than α. C) Reject H0 because the P-value is less than or equal to α. D) Fail to reject H0 because the P-value is greater than α. b) Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A) The percentage of adults that would erase all of their personal information online if they could is more than 52%. B) There is not sufficient evidence to support the claim that the percentage of adults taht would erase all of their personal information online if they could is more than 52%. C) The percentage of adults that would erase all of their personal information online if they could is less than or equal to 52%. D) There is sufficient evidence to supppor the claim that the percentage of adults that would erase all of their personal information online if they could is more than 52%.

a) State a conclusion about the null hypothesis (Reject H0 or fail to reject H0.) Choose the correct answer below. C) Reject H0 because the P-value is less than or equal to α. b) Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? D) There is sufficient evidence to supppor the claim that the percentage of adults that would erase all of their personal information online if they could is more than 52%.

Assume a significance level of α=0.1 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The mean pulse rate​ (in beats per​ minute) of a certain group of adult males is 69 bpm. The hypothesis test results in a​ P-value of 0.0874. a) State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H0​.) Choose the correct answer below. A) Reject H0 because the P-value is less than or equal to α. B) Reject H0 because the P-value is greater than α. C) Fail to reject H0 because the P-value is less than or equal to α. D) Fail to reject H0 because the P-value is greater than α. b) Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion? A) There is sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute) of the group of adult males is 69 bpm. B) The mean pulse rate​ (in beats per​ minute) of the group of adult males is not 69 bpm. C) There is not sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute) of the group of adult males is 69 bpm. D) The mean pulse rate​ (in beats per​ minute) of the group of adult males is 69 bpm.

a) State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H0​.) Choose the correct answer below. A) Reject H0 because the P-value is less than or equal to α. b) Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion? A) There is sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute) of the group of adult males is 69 bpm.

Assume a significance level of α=0.01 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The standard deviation of pulse rates of a certain group of adult males is more than 14 bpm. The hypothesis test results in a​ P-value of 0.3619. a) State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H0​.) Choose the correct answer below. A) Reject H0 because the P-value is greater than α. B) Fail to reject H0 because the P-value is less than or equal to α. C) Reject H0 because the P-value is less than or equal to α. D) Fail to reject H0 because the P-value is greater than α. b) Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion? A) The standard deviation of pulse rates of the group of adult males is less than or equal to 14 bpm. B) There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm. C) The standard deviation of pulse rates of the group of adult males is more than 14 bpm. D) There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm.

a) State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H0​.) Choose the correct answer below. D) Fail to reject H0 because the P-value is greater than α. b) Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion? B) There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm.