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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- The 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 Compare these results to the actual mean μ=$1.502 and standard deviation σ=$1.031.A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44.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, u, 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 4 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? H, :0 OIn the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 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) What is/are the critical value(s)?In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Katy takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. g) What is the interpretation (not your conclusions) of the p value in the context of the problem you found in part e? h) What are your conclusions in the context of the problem? Relate your conclusions to the test statistic and critical value, confidence interval and p value.Gn. don't provide handwriting solution3.2/2There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n1 = 16, x1 ≈ 4.73, and s1 = 2.84 and for region II, n2 = 15, x2 ≈ 3.93, and s2 = 2.45. The two sample standard deviations are sufficiently close that we can assume ?1 = ?2. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) t =You suspect that people living in urban areas produce on average more garbage (X)than those living in rural areas (Y). To verify this opinion, you draw two samples and collect information on the amount of garbage produced in a month (measured in kilos). The first sample, made of 8 subjects living in an urban area, provides a sample mean equal to 40.5 and a sample standard deviation equal to 5.6; in the second sample, made of 10 subjects living in rural areas, the sample mean is 35.6 and the sample standard deviation is 7.5. It is assumed that the two populations are normal with the same unknown variance.Test the null hypothesis that the two population means are equal against a one-sided alternative according to which people living in urban areas produce on average more garbage than those living in rural areas. Use a 1% significance level.A hiring company claims that the variance of the annual salaries for managers is greater in Florida than Georgia. You select a sample of 28 managers in Florida and find the standard deviation to be $11,000. You select a sample of 24 managers in Georgia and find the standard deviation to be $9,200. At α=0.05, can you support the hiring company's claim?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) OA 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 39 hours and that the standard deviation is 4 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? H : μ 2 44 0 H₁ : µ < 44 1 (b) Suppose that we decide to reject the null hypothesis. What sort of error might we be making? Type I (c) Suppose the true mean number of hours worked by software engineers is 44 hours. Fill in the blanks to describe a Type I error. A Type I error would be when, in fact, μ is the hypothesis that u is 3 OThe salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players’ salaries and 35 football players’ salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the shape of the sampling distribution for ? skewed right since the populations are both right skewed skewed right since the differences in salaries cannot be negative approximately Normal since both sample sizes are greater than 30 approximately Normal since the sum of the sample sizes is greater than 30SEE 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. 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