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# (Solved) MATH225 Week 7 Assignment Hypothesis Test for the Mean – Population Standard Deviation Known

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Question

Jamie, a bowler, claims that her bowling score is less thanÂ 168Â points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at aÂ 1%Â significance level, to persuade them. She bowlsÂ 17Â games. The mean score of the sample games isÂ 155Â points. Jamie knows from experience that the standard deviation for her bowling score isÂ 19Â points.

• H0:Â Î¼â‰¥168;Â Ha:Â Î¼<168
• Î±=0.01(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Lexie, a bowler, claims that her bowling score is more thanÂ 140Â points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at aÂ 5%Â significance level, to persuade them. She bowlsÂ 18Â games. The mean score of the sample games isÂ 155Â points. Lexie knows from experience that the standard deviation for her bowling score isÂ 17Â points.

• H0:Â Î¼â‰¤140;Â Ha:Â Î¼>140
• Î±=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Jamie, a chef, claims that her meatball weight is more thanÂ 3Â ounces, on average. Several of her customers do not believe her, so she decides to do a hypothesis test, at aÂ 5%Â significance level, to persuade them. She cooksÂ 13Â meatballs. The mean weight of the sample meatballs isÂ 3.6Â ounces. Jamie knows from experience that the standard deviation for her meatball weight isÂ 0.5Â ounces.

• H0:Â Î¼â‰¤3;Â Ha:Â Î¼>3
• Î±=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Suppose a bowler claims that her bowling score is less thanÂ 116Â points, on average. Several of her teammates do not believe her, so the bowler decides to do a hypothesis test, at aÂ 5%Â significance level, to persuade them. She bowlsÂ 25Â games. The mean score of the sample games isÂ 103Â points. The bowler knows from experience that the standard deviation for her bowling score isÂ 19Â points.

• H0:Â Î¼â‰¥116;Â Ha:Â Î¼<116
• Î±=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Which of the following results in a null hypothesisÂ pâ‰¤0.61Â and alternative hypothesisÂ p>0.61?

## Question

Which graph below corresponds to the following hypothesis test?

H0:Î¼â‰¥5.9,Â Ha:Î¼<5.9

Question

Which of the following results in a null hypothesisÂ pâ‰¥0.44Â and alternative hypothesisÂ p<0.44?

An online article is trying to show that less than 44% of internet users participate in social media, contrary to an established figure saying that at least 44% of internet users participate in social media.

Question

Determine the Type II error if the null hypothesis,Â H0, is: a wooden ladder can withstand weights ofÂ 250Â pounds and less.

• You think the ladder can withstand weight ofÂ 250Â pounds and less when, in fact, it cannot.
• You think the ladder cannot withstand weight ofÂ 250Â pounds and less when, in fact, it really can.
• You think the ladder can withstand weight ofÂ 250Â pounds and less when, in fact, it can.
• You think the ladder cannot withstand weight ofÂ 250Â pounds and less when, in fact, it cannot.

Question

Which graph below corresponds to the following hypothesis test?
H0:pâ‰¤8.1,Â Ha:p>8.1

Question

Determine the Type I error if the null hypothesis,Â H0, is: an electrician claims that no more thanÂ 10%Â of homes in the city are not up to the current electric codes.

• The electrician thinks that no more thanÂ 10%Â of homes in the city are not up to the current electrical codes when, in fact, there really are no more thanÂ 10%Â that are not up to the current electric codes.
• The electrician thinks that more thanÂ 10%Â of the homes in the city are not up to the current electrical codes when, in fact, there really are more thanÂ 10%Â of the homes that do not meet the current electric codes.
• The electrician thinks that more thanÂ 10%Â of the homes in the city are not up to the current electrical codes when, in fact, at mostÂ 10%Â of the homes in the city are not up to the current electric codes.
• The electrician thinks that no more thanÂ 10%Â of homes in the city are not up to the current electrical codes when, in fact, more thanÂ 10%Â of the homes are not up to the current electric codes.

Question

Which of the following results in a null hypothesisÂ pâ‰¤0.69Â and alternative hypothesisÂ p>0.69?

• A mechanic wants to show that the percentage of car owners that follow a normal maintenance schedule is notÂ 69%, contrary to a study that found that the percentage wasÂ 69%.
• A mechanic wants to show that more thanÂ 69%Â of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at mostÂ 69%.
• A mechanic wants to show that at mostÂ 69%Â of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was more thanÂ 69%.
• A mechanic wants to show that less thanÂ 69%Â of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at leastÂ 69%.

Question

Which of the following results in a null hypothesisÂ pâ‰¤0.47Â and alternative hypothesisÂ p>0.47?

Question

Which of the following results in a null hypothesisÂ Î¼â‰¤7Â and alternative hypothesisÂ Î¼>7?

• A study wants to show that the mean number of hours of sleep the average person gets each day is at leastÂ 7.
• A study wants to show that the mean number of hours of sleep the average person gets each day isÂ 7.
• A study wants to show that the mean number of hours of sleep the average person gets each day is more thanÂ 7.
• A study wants to show that the mean number of hours of sleep the average person gets each day is at mostÂ 7.

Question

Suppose the null hypothesis,Â H0, is: a sporting goods store claims that at leastÂ 70%Â of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario?

• The sporting goods store thinks that less thanÂ 70%Â of its customers do not shop at any other sporting goods stores when, in fact, less thanÂ 70%Â of its customers do not shop at any other sporting goods stores.
• The sporting goods store thinks that at leastÂ 70%Â of its customers do not shop at any other sporting goods stores when, in fact, at leastÂ 70%Â of its customers do not shop at any other sporting goods stores.
• The sporting goods store thinks that less thanÂ 70%Â of its customers do not shop at any other sporting goods stores when, in fact, at leastÂ 70%Â of its customers do not shop at any other sporting goods stores.
• The sporting goods store thinks that at leastÂ 70%Â of its customers do not shop at any other sporting goods stores when, in fact, less thanÂ 70%Â of its customers do not shop at any other sporting goods stores.

Question

Determine the Type II error if the null hypothesis,Â H0, is: researchers claim thatÂ 65%Â of college students will graduate with debt.

• The researchers think that greater than or less thanÂ 65%Â of college students will graduate with debt when, in fact,Â 65%Â will graduate with debt.
• The researchers think thatÂ 65%Â of college students will graduate with debt when, in fact, more or less thanÂ 65%Â of college students will graduate with debt.
• The researchers think thatÂ 65%Â of college students will graduate with debt when, in fact,Â 65%Â of college students really will graduate with debt.
• The researchers think that greater than or less thanÂ 65%Â of college students will graduate with debt when, in fact, greater than or less thanÂ 65%Â of college students will graduate with debt.

Question

Which graph below corresponds to the following hypothesis test?
H0:Î¼â‰¤16.9,Â Ha:Î¼>16.9

Question

Which of the hypothesis tests listed below is a left-tailed test? Select all correct answers.

Select all that apply:

• H0:Î¼â‰¥18, Ha:Î¼<18
• H0:Î¼â‰¤19.3, Ha:Î¼>19.3
• H0:Î¼=8, Ha:Î¼â‰ 8
• H0:Î¼â‰¥11.3, Ha:Î¼<11.3
• H0:Î¼â‰¥3.7, Ha:Î¼<3.7

Question

Suppose a pitcher claims that her pitch speed is not equal toÂ 45Â miles per hour, on average. Several of her teammates do not believe her, so the pitcher decides to do a hypothesis test, at aÂ 1%Â significance level, to persuade them. She throwsÂ 21Â pitches. The mean speed of the sample pitches isÂ 46Â miles per hour. The pitcher knows from experience that the standard deviation for her pitch speed isÂ 6Â miles per hour.

• H0:Â Î¼=45;Â Ha:Â Î¼â‰ 45
• Î±=0.01(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

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