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(Answer) MATH399N – Week 7 Assignment: Week 7 – Developing Hypothesis and Understanding Possible Conclusions for Mean

Question 1

Identify the type of hypothesis test below.

H0:X=10.2, Ha: X>10.2

Question 2

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

  1. H0: μ=18, Ha: μ<18
  2. H0: μ=19.3, Ha: μ>19.3
  3. H0: μ=8, Ha: μ≠8
  4. H0: μ=11.3, Ha: μ<11.3
  5. H0: μ=3.7, Ha: μ<3.7

Question 3

Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters.

  • H0: μ=174; Ha: μ>174
  • α=0.1(significance level)

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

Question 4

A city wants to show that the mean number of public transportation users per day is more than 5,575. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.

  1. H0: μ=5,575; Ha: μ<5,575
  2. H0: μ=5,575; Ha: μ≥5,575
  3. H0: μ=5,575; Ha: μ>5,575
  4. H0: μ=5,575; Ha: μ≠5,575

Question 5

Which of the following results in a null hypothesis p=0.44 and alternative hypothesis p<0.44?

  1. 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 44% of internet users participate in social media.
  2. An online article is trying to show that 44%of internet users participate in social media, contrary to an established figure saying that more than 44% of internet users participate in social media.
  3. An online article is trying to show that more than 44%of internet users participate in social media, contrary to an established figure saying 44% of internet users participate in social media.
  4. An online article is trying to show that at least 44%of internet users participate in social media, contrary to an established figure saying that less than 44% of internet users participate in social media.

Question 6

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

And, the alternative hypothesis, Ha, is: the percentage of homes in the city that are not up to the current electric codes is more than 10%.

  1. There is insufficient evidence to conclude that more than 10%of homes in the city are not up to the current electrical codes when, in fact, there are more than 10% that are not up to the current electric codes.
  2. There is insufficient evidence to conclude that less than 10%of homes in the city are not up to the current electrical codes when, in fact, there are less than 10% that are not up to the current electric codes.
  3. There is sufficient evidence to conclude that more than 10%of homes in the city are not up to the current electrical codes when, in fact, there are no more than 10% that are not up to the current electric codes.
  4. There is sufficient evidence to conclude that less than 10%of homes in the city are not up to the current electrical codes when, in fact, there are at least 10% that are not up to the current electric codes.

Question 7

Jolyn, a golfer, claims that her drive distance is not equal to 222 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She hits 11 drives. The mean distance of the sample drives is 218 meters. Jolyn knows from experience that the standard deviation for her drive distance is 14 meters.

  • H0: μ=222; Ha: μ≠222
  • α =0.05(significance level)

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

Question 8

Suppose the null hypothesis, H0, is at least 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

And the alternative hypothesis, Ha, is less than 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

What is the Type I error in this scenario?

  1. The sporting goods store cannot conclude that less than 70%of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.
  2. The sporting goods store cannot conclude that at least 70%of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.
  3. The sporting goods store concludes that less than 70%of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.
  4. The sporting goods store concludes that less than 70%of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.

Question 9

Which of the following results in a null hypothesis p=0.69 and alternative hypothesis p>0.69?

  1. A mechanic wants to show that the percentage of car owners that follow a normal maintenance schedule is not 69%, contrary to a study that found that the percentage was 69%.
  2. A mechanic wants to show that more than 69%of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at most 69%.
  3. A mechanic wants to show that at most 69%of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was more than 69%.
  4. A mechanic wants to show that less than 69%of car owners follow a normal maintenance schedule, contrary to a study that found that the percentage was at least 69%.

Question 10

A mechanic wants to show that more than 44% of car owners do not follow a normal maintenance schedule. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.

H0: p=0.44; Ha: p>0.44

H0: p=0.44; Ha: p≥0.44

H0: p=0.44; Ha: p≤0.44

H0: p=0.44; Ha: p<0.44

Question 11

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

  • H0: μ=140; Ha: μ>140
  • α=0.05(significance level)

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

Question 12

Floretta, a pitcher, claims that her pitch speed is less than 46 miles per hour, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She throws 24 pitches. The mean speed of the sample pitches is 37 miles per hour. Floretta knows from experience that the standard deviation for her pitch speed is 5 miles per hour.

  • H0: μ=46; Ha: μ<46
  • α=0.05(significance level)

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

Question 13

Suppose the null hypothesis, H0, is: no more than 70% of customers at a sporting goods store do not shop at any other sporting goods stores.

And the alternative hypothesis, Ha, is: the sporting goods store claims more than 70% of its customers do not shop at any other sporting goods stores.

What is β, the probability of a Type II error in this scenario?

  1. The probability that the sporting goods store can conclude that more than 70%of its customers do not shop at any other sporting goods stores when, in fact, more than 70% of its customers do not shop at any other sporting goods stores.
  2. The probability that the sporting goods store can conclude that more than 70%of its customers do not shop at any other sporting goods stores when, in fact, no more than 70% of its customers do not shop at any other sporting goods stores.
  3. The probability that the sporting goods store cannot conclude that more than 70%of its customers do not shop at any other sporting goods stores when, in fact, no more than 70% of its customers do not shop at any other sporting goods stores.
  4. The probability that the sporting goods store cannot conclude that more than 70%of its customers do not shop at any other sporting goods stores when, in fact, more than 70% of its customers do not shop at any other sporting goods stores.

Question 14

Which graph below corresponds to the following hypothesis test?

H0:p=8.1, Ha:p>8.1

Question 15

Is the test below left-, right-, or two-tailed?

H0: p=0.39, Ha: p≠0.39

  1. The hypothesis test is two-tailed.
  2. The hypothesis test is left-tailed.
  3. The hypothesis test is right-tailed.

Question 16

Suppose the null hypothesis, H0, is: a surgical procedure is successful at least 80% of the time. What is the Type I error in this scenario?

  1. Doctors think the surgical procedure is successful less than 80%of the time when, in fact, it really is successful less than 80% of the time.
  2. Doctors think the surgical procedure is successful less than 80%of the time when, in fact, it is successful at least 80% of the time.
  3. Doctors think the surgical procedure is successful at least 80%of the time when, in fact, it is not.
  4. Doctors think the surgical procedure is successful at least 80%of the time when, in fact, it is.

Question 17

Determine the Type I error if the null hypothesis, H0, is: 65% of college students will graduate with debt.

And, the alternative hypothesis, Ha, is: that researchers claim more than 65% of college students will graduate with debt.

  1. The researchers conclude that more than 65%of college students will graduate with debt when, in fact, 65% will graduate with debt.
  2. The researchers cannot conclude that more than 65%of college students will graduate with debt when, in fact, 65% will graduate with debt.
  3. The researchers conclude that 65%of college students will graduate with debt when, in fact, more than 65% will graduate with debt.
  4. The researchers cannot conclude that 65%of college students will graduate with debt when, in fact, more than 65% will graduate with debt.

SOLUTIONS:

Question 1

Identify the type of hypothesis test below.

H0:X=10.2, Ha: X>10.2

Answer

The hypothesis test is right-tailed.

Question 2

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

  1. H0: μ=18, Ha: μ<18
  2. H0: μ=19.3, Ha: μ>19.3
  3. H0: μ=8, Ha: μ≠8
  4. H0: μ=11.3, Ha: μ<11.3
  5. H0: μ=3.7, Ha: μ<3.7

Answer

H0: μ=18, Ha: μ<18

H0: μ=11.3, Ha: μ<11.3

H0: μ=3.7, Ha: μ<3.7

Question 3

Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters.

  • H0: μ=174; Ha: μ>174
  • α=0.1(significance level)

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

Answer

Test statistic = 3.87​

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