A simulated exercise gave n = 28 observations on escape time (sec) for oil workers, from which the sample mean and sample standard deviation are 372.76 and 22.85, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 min. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using a significance level of 0.05.
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- You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes. Perform a hypothesis test to determine if there’s evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes by answering the following questions: (a) What are the null and alternate hypotheses for this test? (b) What is the value of the test statistic for this test? (c) Using the critical value approach, at the 0.05 level of significance, what is the decision rule? (d) What is your conclusion in context of the problem? (Answer this question in a complete sentence(s) and include why, referring to the decision rule.) (e) Using the p-value approach, at the…A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality. A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality. 0.0067 0.0135 0.9962 0.9933A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 16 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.97 ounces and 0.24 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, µ, differs from 8 ounces? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 Hị :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO O20 |(c) Find the value of the test statistic. (Round to three or more decimal places.) OIn a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The ← changes (before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.7 and a standard deviation of 18.8. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. What is the confidence interval estimate of the population mean μ? mg/dL. <μ< mg/dL (Round to two decimal places as needed.). What does the confidence interval suggest about the effectiveness of the treatment? ... OA. The confidence interval limits contain 0, suggesting…An electronics production sequence includes a process where a film of metal is deposited on a board. The film must be more than 1.000 mm thick. If the film is too thin the process fails. The engineer ran a test where the null hypothesis was that the mean thickness was at most 1.000 mm. A sample of 100 boards had a mean thickness of 1.007 mm and a standard deviation of 0.050 mm.At what level of significance would the null hypothesis be rejected? Express your answer at a decimal (not a percent) rounded to three places.In a test of the effectiveness of garlic for lowering cholesterol,44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes(beforeminus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.6 and a standard deviation of 17.5. Construct a 99%confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? What is the confidence interval estimate of the population mean mu? mg/dLless than muless than mg/dL (Round to two decimal places as needed.)In tests of a computer component, it is found that the mean time between failures is 909 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 25 modified components produce a mean time between failures of 955 hours. Using a 1% level of significance, perform a hypothesis test to determine whether the mean time between failures for the modified components is greater than 909 hours. Assume that the population standard deviation is 53 hours.A simulated exercise gave n = 26 observations on escape time (sec) for oil workers, from which the sample mean and sample standard deviation are 371.15 and 23.02, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 min. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using a significance level of 0.05. USE SALT State the appropriate hypotheses. Ho: μ = 360 Ha: μ 360 Ho: μ = 360 H₂H ≤ 360 Ho: μ = 360 H₂: μ = 360 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? O Do not reject the null hypothesis. There is not sufficient evidence that true average escape time exceeds 6 min. O Do not reject the null hypothesis. There is sufficient evidence that true average escape time exceeds 6 min. O Reject the null hypothesis. There is sufficient evidence that…A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.14 ounces and 0.23 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, μ , differs from 8 ounces? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The two critical values at the 0.05 level…The mean length of steel bolts from a manufacturing process is advertised as 15.1 mm. An inspector believes that this value is not correct. To investigate the inspector's claim, the lengths of a random sample of size 280 bolts are measured and found to have a sample mean of 15.6 mm. We will assume that the population of bolt lengths is normally distributed with standard deviation of 5.0 mm. Test whether the mean population length has changed at a level of significance of 10%. Show your relevant steps below. Step 1: Hypotheses: • The null hypothesis Ho is (choose one): = 5.0 u = u = 15.1 OH = 15.6 u = 280.0 • For the alternative hypothesis H. we change the equal sign in Ho to (choose one): Step 2: Rejection Region: The rejection region is bounded by the following critical values: Critical z value(s) =A coin- ed drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 13 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.96 ounces and 0.14 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, u, differs from 7 ounces? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. p H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) OIn a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before minus−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 4.3 and a standard deviation of 18.6. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?what is the confidence interval estimate of the population meanRecommended 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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