Regardless of the shape of the population, the sampling distribution of the mean approaches a normal distribution as sample size increases А. True В. False
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- Steve, the underpaid graduate student, is interested in determining how many final grades in Dr. Boehring’sclass vary. Steve determines that the standard deviation of final grades in Dr. Tahkstumusch’s class is 7. Steve takes a random sample of 50 final grades from Dr. Boehring’s class and computes a standard deviation of 9.Assume that the final grades in Dr. Boehring’s class are normally distributed. At the 5% significance level, do the data provide sufficient evidence to conclude that the standard deviationσof final grades in Dr. Boehring’sclass are greater than 7? Use the rejection region approach for all of the parts below. (a) Define the appropriate hypotheses (b)State and verify that the proper assumptions hold (c)Use the rejection region approach to perform the test (d) Provide support for your decision regarding the null hypothesis (e) Write a summary of your conclusion in the context of the problemThe weight in kilograms of the citizens of Fredonia has a mean of 50 kg and standard deviation of 24 kg (a) Find the mean of the sampling distribution of the sample mean. (b) Find the standard deviation of the sampling distribution of the sample mean.In a Normal Distribution with the Mean of 77 and the Standard Deviation of 5 , find P ( x>66)
- The measurement of the distance to a certain object is accompanied by systematic and random errors. The systematic error equals 50 m. in the direction of decreasing distance. The random errors obey the normal distribution law with the mean-square deviation = 100 m. Find (1) the probability of measuring the distance with an error not exceeding 150 m. in absolute value, (2) the probability that the measured distance does not exceed the actual one.A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the α=0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired t-test is reasonable. Observation 1 2 3 4 5 6 Height of father (in inches) 70.1 74.5 69.5 65.1 69.6 65.9 Height of son (in inches) 69.5 75.9 71.7 69.4 71.5 70.7 What are the hypotheses for the t-test? Note that population 1 is fathers and population 2 is sons. A. H0: μ1=μ2 Ha: μ1<μ2 B. H0: μ1=μ2 Ha: μ1≠μ2 C. H0: μ1=μ2 Ha: μ1>μ2 D. H0: μ1≥μ2 Ha: μ1<μ2A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At a = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient Total Blood Cholesterol (Before) Total Blood Cholesterol (After) OA. Ho Hd #0 HA Hd=0 OC. Ho Hd ≤0 HA Hd >0 Calculate the standardized test statistic t= (Round to three decimal places as needed.) Calculate the P-value P-value= (Round to four decimal places as needed) State the conclusion. 1 205 204 Ho. There C 2 225 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be…