MATH 225N Week 7 Assignment: Hypothesis Test for the Mean – Population Standard Deviation Known
1. Jamie, a bowler, claims that her bowling score is
... [Show More] less than 168 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She bowls 17 games. The mean score of the sample games is 155 points. Jamie knows from experience that the standard deviation for her bowling score is 19 points.
• H0: μ≥168; Ha: μ<168
• α=0.01 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
−2.82.
2. Which of the following results in a null hypothesis p≤0.61 and alternative hypothesis p>0.61?
A study says that at most 61% of students study less than 5 hours per week. A researcher thinks this is incorrect, and wants to show that more than 61% of students study less than 5 hours per week.
3. 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?
3.74
4. Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less.
You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot.
5. Which of the following results in a null hypothesis p=0.3 and alternative hypothesis p≠0.3?
An insurance company claims that 30% of adults between the ages of 30 and 40 are overweight. A group of doctors think that is not accurate, and wants to show that the percent of these adults that are overweight is not 30%.
6. Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes.
The electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, at most 10% of the homes in the city are not up to the current electric codes.
7. Which graph below corresponds to the following hypothesis test?
H0:μ≥5.9, Ha:μ<5.9
8. Which graph below corresponds to the following hypothesis test?
H0:p≤8.1, Ha:p>8.1
9. Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% 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 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.
10. Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt.
The researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65% of college students will graduate with debt.
11. Which graph below corresponds to the following hypothesis test?
H0:μ≤16.9, Ha:μ>16.9
12. Which of the hypothesis tests listed below is a left-tailed test? Select all correct answers.
Correct answer:
H0:μ≥18 , Ha:μ<18
H0:μ≥11.3 , Ha:μ<11.3
H0:μ≥3.7 , Ha:μ<3.7
Remember the forms of the hypothesis tests.
• Right-tailed: H0:μ≤μ0 , Ha:μ>μ0 .
• Left-tailed: H0:μ≥μ0 , Ha:μ<μ0 .
• Two-tailed: H0:μ=μ0 , Ha:μ≠μ0 .
So in this case, the left-tailed tests are:
• H0:μ≥3.7 , Ha:μ<3.7
• H0:μ≥18 , Ha:μ<18
• H0:μ≥11.3 , Ha:μ<11.3
13. Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Correct answer:
The researchers think that greater than or less than 65% of college students will graduate with debt when, in fact, 65% will graduate with debt.
14. A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative hypothesis, Ha, is that the seat belt can hold less than 5000 pounds of force. What is a Type II error in this scenario?
The researchers conclude that the seat belt holds at least 5000 pounds of force, but the seat belt actually holds less than 5000 pounds.
15. Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 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?
the probability that the sporting goods store thinks that at least 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
16. Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80% of the time. Which of the following gives β, the probability of a Type II error?
The probability that doctors think the surgical procedure is successful at least 80% of the time when, in fact, it is not
17. A car magazine claims that 68% of car owners follow a normal maintenance schedule. A mechanic does not think this is accurate, and so he wants to show that the percentage of people who follow a normal maintenance schedule is not equal to 68%.
Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p.
H0: p=0.68; Ha: p≠0.68
18. Which of the following results in a null hypothesis p≤0.62 and alternative hypothesis p>0.62?
A car magazine claims that at most 62% of car owners follow a normal maintenance schedule. A mechanic does not think this is right, and wants to show that more than 62% of car owners follow a normal maintenance schedule.
19. Which of the following results in a null hypothesis μ≥31 and alternative hypothesis μ<31?
A hospital claims that the mean wait time for emergency room patients is at least 31 minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is less than 31 minutes.
20. Which of the following results in a null hypothesis μ≤7 and alternative hypothesis μ>7?
A study wants to show that the mean number of hours of sleep the average person gets each day is more than 7
21. Which of the following answers give valid null and alternative hypotheses for a hypothesis test?
H0: μ≥15; Ha: μ<15 H0: μ=15; Ha: μ≠15
22. A mattress store advertises that their beds last at least 5 years, on average. A consumer group thinks that they do not last that long and wants to set up a hypothesis test.
If μ denotes the average time, in years, that the mattresses last, what are the null and alternative hypotheses in this situation?
H0: μ≥5; Ha: μ<5
23. Which of the following results in a null hypothesis p≥0.44 and alternative hypothesis p<0.44?
24. Which of the following results in a null hypothesis p≥0.44 and alternative hypothesis 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.
25. Suppose a pitcher claims that her pitch speed is not equal to 45 miles per hour, on average. Several of her teammates do not believe her, so the pitcher decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 21 pitches. The mean speed of the sample pitches is 46 miles per hour. The pitcher knows from experience that the standard deviation for her pitch speed is 6 miles per hour.
• H0: μ=45; Ha: μ≠45
• α=0.01 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
0.76
26. Suppose a bowler claims that her bowling score is less than 116 points, on average. Several of her teammates do not believe her, so the bowler decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 25 games. The mean score of the sample games is 103 points. The bowler knows from experience that the standard deviation for her bowling score is 19 points.
• H0: μ≥116; Ha: μ<116
• α=0.05 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
-3.42
27. Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type II error in this scenario?
You think the mean age of the horses on a ranch is 6 years when, in fact, it is not.
28. Suppose the null hypothesis, H0, is: a weightlifting bar can withstand weights of 800 pounds and less. What is the Type I error in this scenario?
You think the weightlifting bar cannot withstand weights of 800 pounds and less when, in fact, it can.
29. Suppose the null hypothesis, H0, is: doctors believe that a surgical procedure is successful at least 80% of the time. What is the Type I error in this scenario?
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.
30. A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, H0, is that the rack can hold at least 100 pounds of force. The alternative hypothesis, Ha, is that the rack can hold less than 100 pounds of force. What is a Type I error in this scenario?
The researchers conclude that the rack holds less than 100 pounds of force, but the rack actually holds more than 100 pounds.
31. What is β, the probability of a Type II error if the null hypothesis, H0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes.
the probability that the electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, more than 10% of the homes are not up to the current electric codes
32. Determine the Type I error if the null hypothesis, H0, is: Carmin believes that her chemistry exam will only cover material from chapters four and five.
Carmin believes that her chemistry exam will not cover material only from chapters four and five when, in fact, it will only cover material from chapters four and five. [Show Less]