## MATH 225N Week 7 Assignment: Hypothesis Test for the Mean – Population Standard Deviation Known

**1. Question: **.Jamie, a bowler, claims that her bowling score is 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 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.

*H*0:*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. Question: **Which of the following results in a null hypothesis *p*≤61 and alternative hypothesis *p*>0.61?

**3. Question: **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 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.

*H*0:*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?

**4. Question: **Determine the Type II error if the null hypothesis, *H*0, is: a wooden ladder can withstand weights of 250 pounds and less.

**5. Question: **Which of the following results in a null hypothesis *p*=3 and alternative hypothesis *p*≠0.3?

**6. Question: **Determine the Type I error if the null hypothesis, *H*0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes.

**7. Question: **Which graph below corresponds to the following hypothesis test?

*H*0:*μ*≥9, *Ha*:*μ*<5.9

**8. Question: **Which graph below corresponds to the following hypothesis test?

*H*0:*p*≤1, *Ha*:*p*>8.1

**9. Question: **Suppose the null hypothesis, *H*0, 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?

**10. Question: **Determine the Type II error if the null hypothesis, *H*0, is: researchers claim that 65% of college students will graduate with debt.

**11. Question: **Which graph below corresponds to the following hypothesis test?

*H*0:*μ*≤9, *Ha*:*μ*>16.9

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

**13. Question: **Determine the Type I error if the null hypothesis, *H*0, is: researchers claim that 65% of college students will graduate with debt.

**14. Question: **A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, *H*0, 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?

**15. Question: **Suppose the null hypothesis, *H*0, 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?

**16. Question: **Suppose the null hypothesis, *H*0, 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?

**17. Question: **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, *H*0, and the alternative hypothesis, *Ha*, in terms of the parameter *p*.*H*0: *p*=0.68; *Ha*: *p*≠0.68

**18. Question: **Which of the following results in a null hypothesis *p*≤62 and alternative hypothesis *p*>0.62?

**19. Question: **Which of the following results in a null hypothesis *μ*≥31 and alternative hypothesis *μ*<31?

**20. Question: **Which of the following results in a null hypothesis *μ*≤7 and alternative hypothesis *μ*>7?

**21. Question: **Which of the following answers give valid null and alternative hypotheses for a hypothesis test?

**22. Question: **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?

**23. Question: **Which of the following results in a null hypothesis *p*≥44 and alternative hypothesis *p*<0.44?

**24. Question: **Which of the following results in a null hypothesis *p*≥44 and alternative hypothesis *p*<0.44?

**25. Question: **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 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.

## STATUS

*H*0:*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?

**26. Question: **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 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.

*H*0: *μ*≥116; *Ha*: *μ*<116

*α*=0.05 (significance level)

**z**-score) of this one-mean hypothesis test, rounded to two decimal places?

**27. Question: **Suppose the null hypothesis, *H*0, is: the mean age of the horses on a ranch is 6 What is the Type II error in this scenario?

**28. Question: **Suppose the null hypothesis, *H*0, is: a weightlifting bar can withstand weights of 800 pounds and less. What is the Type I error in this scenario?

**29. Question: **Suppose the null hypothesis, *H*0, is: doctors believe that a surgical procedure is successful at least 80% of the time. What is the Type I error in this scenario?

**30. Question: **A consumer protection company is testing a towel rack to see how much force it can hold. The null hypothesis, *H*0, 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?

**31. Question: **What is *β*, the probability of a Type II error if the null hypothesis, *H*0, 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. Question: **Determine the Type I error if the null hypothesis, *H*0, is: Carmin believes that her chemistry exam will only cover material from chapters four and five.