BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of 3200 hours. Suppose we have good reason to believe that μ is different from 3200 hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 3380 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H and the alternative hypothesis H₁ that should be used for the test? μ x H 1 (b) Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? Type I (c) Suppose the true mean lifetime of BIG's light bulbs is 3200 hours. Fill in the blanks to describe a Type I error. A Type I error would be rejecting the hypothesis that u is less than or equal to ▼ 600 when, in fact, μ is equal to 3380 □□ □□ ロ=ロ 밈 □<ロ □≠□ G
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- In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of 2800 hours. Suppose we have good reason to believe that μ is different from 2800 hours and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2600 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? Ho :O H₁ :0 (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? (Choose one) ▼ (c) Suppose the true mean lifetime of BIG's light bulbs is 2800 hours. Fill in the blanks to describe a Type I error. (Choose one) A Type I error would be (Choose one) the hypothesis that u is (Choose one) when, in fact, μ is (Choose one) ▼ μ 0<0 X X OSO ΠΣΠ 0=0 5 ロ<ロ SA somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, μ, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 48 hours and that the standard deviation is 6 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test? (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? (c) Suppose the true mean number of hours worked by software engineers is 50 hours. A Type II error would be _____ the hypothesis that μ is_____ when, in fact, μ is_____ .
- In the year 2032, Katie Ruff is a leading traveling nurse. Katie is interested in reducing the mean recovery time for patients after experiencing a serious injury. Suppose the mean recovery time is presently 8.4 months. Katie takes a random sample of 45 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 7.9 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) Using the appropriate level of confidence, what is the confidence interval? d) What is the interpretation (not your conclusions) in the context of the problem of the confidence interval you obtained in part c? e) What is the p value? f) What is the interpretation (not your conclusions) of the p value in the context of the problem you found in part…A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, μ, is now less than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 40 hours and that the standard deviation is 5 hours. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H, that should be used for the test? Ho : D H₁:0 (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? (Choose one) (c) Suppose the true mean number of hours worked by software engineers is 38 hours. Fill in the blanks to describe a Type II error. 20 F3 A Type II error would be (Choose one) ▼ the hypothesis that µ is (Choose one) Continue F4 (Choose one) ▼when, in fact, μ is (Choose one) F5 MacBook Air F6 A F F7The frequency distribution was obtained using a class width of 0.5 for data on cigarette tax rates. Use the frequency distribution to approximate the population mean and population standard deviation. Compare these results to the actual mean μ=$1.502 and standard deviation σ=$1.031.In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. The lowest score that would qualify a student for an A is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a B is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a C is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a D is nothing. (Round up to the nearest integer as needed.)The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.961 g and a standard deviation of 0.318 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine.In what range would you expect to find the middle 50% of amounts of nicotine in these cigarettes (assuming the mean has not changed)? Between Correct and Correct.If you were to draw samples of size 58 from this population, in what range would you expect to find the middle 50% of most average amounts of nicotine in the cigarettes in the sample? Between and .Enter your answers as numbers. Your answers should be accurate to 4 decimal places.In a certain country the heights of adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.5 inches. The country's military requires that men have heights between 65 inches and 76 inches. Determine what percentage of this country's men are eligible for the military based on height. The percentage of men that are eligible for the military based on height is (Round to two decimal places as needed.) %. (1) U +A population has a mean µ = 70 and a standard deviation o = 28. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 261. P = (Simplify your answer.) = (Type an integer or decimal rounded to three decimal places as needed.)In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 73 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, μ, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 47 hours and that the standard deviation is 6 hours. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H₁ that should be used for the test? μ x Н. : H₁ : (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? (Choose one) (c) Suppose the true mean number of hours worked by software engineers is 49 hours. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) when, in fact, is (Choose one) ▼the hypothesis that μ is (Choose one) (Choose one) OSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. 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