Hypothesis Test for the Mean - Population Standard Deviation Known week 7

Hypothesis Test for the Mean - Population Standard Deviation Known/week 7 1. 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 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 61 % of students study less than and alternative hypothesis A study says that at most researcher thinks this is incorrect, and wants to show that more than hours per week. A % of students study less than hours per week. p>0.61? p≤0.61 61 5 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. H0, is: a wooden ladder can withstand 250 You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot. 5 Determine the Type II error if the null hypothesis, weights of pounds and less. 5. 6. than 10% electric codes. 30 10 10 p=0.3 H0 p≠0.3? 30 and 40 are Which of the following results in a null hypothesis 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 Determine the Type I error if the null hypothesis, 7. Which graph below corresponds to the following hypothesis test? H0:μ≥5.9, Ha:μ<5.9 % of adults between the ages of 30%. and alternative hypothesis An insurance company claims that , is: an electrician claims that no more of homes in the city are not up to the current electric codes. % of the homes in the city are not up to the current The electrician thinks that more than % of the homes in the city are not up to the current electrical codes when, in fact, at most 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 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. H0 65%of 65 with debt. 11. Which graph below corresponds to the following hypothesis test? scenario? The sporting goods store thinks that less than Determine the Type II error if the null hypothesis, , is: researchers claim that 65 % of college students college students will graduate with debt. The researchers think that % of college students will graduate will graduate with debt when, in fact, more or less than H0:μ≤16.9, Ha:μ>16.9 12. left-tailed Which of the hypothesis tests listed below is a Correct answer: H0:μ≥18 H0:μ≥11.3 , Ha:μ<18 Ha:μ<11.3 test? Select all correct answers. , 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: 13. 65% answer: H0 Correct • H0:μ≥3.7 , Ha:μ<3.7 • H0:μ≥18 , Ha:μ<18 • H0:μ≥11.3 , Ha:μ<11.3 Determine the Type I error if the null hypothesis, 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? 15. 16. H0 70% β, the Suppose the null hypothesis, stores when, in fact, less than 70 , is: a sporting goods store claims that at least of its customers do not shop at any other sporting goods stores. What is probability of a Type II error in this scenario? the probability that the sporting goods % of its customers do not shop at any other sporting goods store thinks that at least % of its customers do not shop at any other sporting goods stores 80% β 70 H0 , is: researchers claim that of college students will graduate with debt. The researchers conclude that the seat belt holds 5000 pounds of force, but the seat belt actually holds less than 5000 pounds. at least Suppose the null hypothesis, , is: doctors believe that a surgical procedure is successful at least of the time. Which of the following gives , the probability of a Type II error? the probability that doctors think the surgical procedure is successful at least 80 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 % of the time when, in fact, it is not =0.68; Ha: p ≠0.68 18. p>0.62? 19. than 31 20. μ>7 p≤0.62 62% of μ≥31 μ<31? μ≤7 Which of the following results in a null hypothesis 62 and alternative hypothesis % of car owners follow a normal maintenance A car magazine claims that at most schedule. A mechanic does not think this is right, and wants to show that more than car owners follow a normal maintenance schedule. Which of the following results in a null hypothesis A hospital claims that the mean wait time for emergency room patients is at least and alternative hypothesis minutes. A group of researchers think this is inaccurate and wants to show that the mean wait time is less 31 minutes. Which of the following results in a null hypothesis 7 and alternative hypothesis ? A study wants to show that the mean number of hours of sleep the average person gets each day is more than 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? 44 44 . 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. H0 6 6 years 28. H0 800 800 An online article is trying to show that less than % of internet users participate in social media, contrary to an established figure saying that at least % of internet users participate in social media Suppose the null hypothesis, , is: the mean age of the horses on a ranch is years. What is the Type II error in this scenario? when, in fact, it is not. You think the mean age of the horses on a ranch is Suppose the null hypothesis, pounds and less. What is the Type I error in this scenario? , is: a weightlifting bar can withstand weights of You think the weightlifting bar cannot withstand weights of pounds and less when, in fact, it can. 29. H0 least 80% 80 80% 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? Suppose the null hypothesis, , is: doctors believe that a surgical procedure is successful at of the time. What is the Type I error in this scenario? % of the time when, in fact, it is successful at least Doctors think the surgical procedure is successful less than of the time. 100 31. β 10 32. 100 H0 H0 10% of The researchers conclude that the rack holds less than pounds of force, but the rack actually holds more than pounds. What is , the probability of a Type II error if the null hypothesis, 10% , is: an electrician claims that no more than of homes in the city are not up to the current electric codes. the probability that the electrician thinks that no more than homes in the city are not up to the current electrical codes when, in fact, more than % of the homes are not up to the current electric codes Determine the Type I error if the null hypothesis, Carmin believes that her chemistry exam will not cover material only from chapters four , is: Carmin believes that her chemistry exam will only cover material from chapters four and five. and five when, in fact, it will only cover material from chapters four and five.