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- A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimete on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that th differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "before - after" differences. Does hypnotism appear to be effective in reducing pain? Before After 4.8 6.3 2.4 2.6A researcher is planning a study of graduate students’ sleep deprivation. Assume that the population mean and standard deviation are provided, and a random sample of 25 students are drawn to participate. What statistical procedure is appropriate for conducting the study? - Z test - Independent samples t-test - Dependent samples t-test - ?Identify the null hypothesis, alternative hypothesis, test statistic, conclusion about the null hypothesis and final conclusion that addresses the original claim. The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9lbs. Assuming that σ is known to be 121.2lb, use a 0.10 significance level to test the claim that the population mean of all such employees' weights is less than 200lb.In a random sample of males, it was found that 24 write with their left hands and 219 do not. In a random sample of females, it was found that 60 write with their left hands and 459 do not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below. O Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of a= 0.01, so males is less than that among females. HEDD the null hypothesis. There evidence to support the claim that the rate of left-handedness amongA manufacturer claims that only 2% of their products are defective. A store receives a delivery of 300 items from the manufacturer. Let p-hat = the proportion of defective items in a sample of 300 items. Assuming the manufacturer is correct that only 2% of their products are defective, what are the mean and standard deviation of the sampling distribution of p-hat ? Options: The mean is 0.02 and the standard deviation is 0.008. The mean is 6 and the standard deviation is 2.42. The mean is 6 and the standard deviation is 5.88. The mean is 0.02 and the standard deviation is 0.196.A random sample of 20 binomial trials resulted in 9 successes. Test claim that the population proportion of successes does not equal 0.50. Use level of significance of 0.05. Can a normal distribution be used for the p distribution? State the hypotheses. Compute p and the corresponding standardized sample test statistic. Find the p value of the test. Do you reject or fail to reject Ho? What do the results tell?Which samples show unequal variances? Use a = .10 in all tests. Show the critical values and degrees of freedom clearly and illustrate the decision rule. s1 = 10.2, n1 = 22, s2 = 6.4, n2 = 16, two-tailed test s1 = .89, n1 = 25, s2 = .67, n2 = 18, right tailed test s1 = 124, n1 = 12, s2 = 260, n2 = 10, left-tailed testmagazine includes a report on the energy costs per year for 32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.37. Assume the sample is taken from a normally distributed population. Construct 98% confidence intervals for (a) the population variance σ2 and (b) the population standard deviation σ. Interpret the resultsWhich distribution do you use to find critical values for confidence intervals (n = 20) for a variancewhen the population standard deviation sigma is unknown?Recommended 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. FreemanMATLAB: 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. Freeman