1. A random sample of n observations is selected from a normal population. Specify the rejection region, test statistic, and conclusion. Ho: μ = 3000 Ha:μ# 3 000 x = 2958 S = 39 n = 8 a = 0.05
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- Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular mu mu 1 mu 2 n 26 26 x overbar 0.79093 lb 0.81234 lb s 0.00433 lb 0.00753 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 greater thanmu 2 B. Upper H 0 : mu 1 equalsmu 2 Upper H 1 : mu 1 less thanmu 2 C. Upper H 0…10. Claim: P₁ = P₂; α = 0.05. Sample statistics: x1 = 265, n₁ - X2 204, 2 - 301, 247 'DUse formulas to solve this and also with explaination
- Sam works at the JJ Electronics Factory. JJ produces the A23 electronic component. The length, X, of an A23, is normally distributed with a meanu = 10 centimeters and a standard deviation o = 0.53 centimeters. Sam randomly selects 20 A23 components from the production line for quality control purposes and measures their lengths. Let M be the sample mean length of the measured A23 components. Let S be the total length of the measured A23 components. (i.e. sum of the 20 lengths. a) What is the probability that X 10.5? .3085 c) What is the probability that all of the 20 measurements are less than 11? .0171 d) What is the expected value of S? 200 e) What is the standard deviation of S? 2.37 f) What is the probability that S-200 >2? 1.99 g) What is the standard deviation of S-200 2.37 h) What is the expected value of M? 10 i) What is the standard deviation of M? .1187 j) What is the probability that M >10.1? .199 k) What is the standard deviation of 9M? 1.068 1) If the probability of X >k…Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Male BMI Female BMI μ μ1 μ2 n 41 41 x 28.3981 26.4624 s 7.246507 5.820596 a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1≥μ2 H1: μ1<μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1>μ2 The test statistic, t, is ______.(Round to two decimal places as needed.) The P-value is _____.(Round to three decimal places as needed.) State the conclusion for the test. A. Fail to reject the null…Suppose you want to test the claim that u, > H,. Two samples are randomly selected from normal populations. The sample statistics are given below. Assume that o #o5. At a level of significance of a = 0.01, when should you reject Ho? n, = 18, n2 =13, x, = 470, x2 = 455, s, = 40, s2 = 25 %3D O A. Reject H, if the standardized test statistic is greater than 2.681. B. Reject Ho if the standardized test statistic is greater than 1.699. O C. Reject H, if the standardized test statistic is greater than 3.055. D. Reject H, if the standardized test statistic is greater than 2.179.
- In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school,70 % were enrolled in college. At a=.009, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e).Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular μ μ1 μ2 n 20 20 x 0.78646 lb 0.80233 lb s 0.00449 lb 0.00755 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1<μ2 The test statistic, t, is nothing. (Round to two decimal places as needed.) The P-value is…The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use ? = 0.01 and assume normality. n = 36, Σd = 227, Σd2 = 6244(a) Find t. (Give your answer correct to two decimal places.)(ii) Find the p-value. (Give your answer correct to four decimal places.)(b) State the appropriate conclusion. Reject the null hypothesis, there is significant evidence that the coating is beneficial.Reject the null hypothesis, there is not significant evidence that the coating is beneficial. Fail to reject the null hypothesis, there is significant evidence that the coating is beneficial.Fail to reject the null hypothesis, there is not significant evidence that the coating is beneficial.
- Women are recommended to consume 1790 calories per day. You suspect that the average calorie intake is smaller for women at your college. The data for the 15 women who participated in the study is shown below: 1959, 1908, 1789, 1544, 1805, 1656, 1899, 1811, 1686, 1688, 1687, 1943, 1612, 1789, 1467 Assuming that the distribution is normal, what can be concluded at the α = 0.05 level of significance? For this study, we should use The null and alternative hypotheses would be: H0: H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly less than 1790 at α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1790. The data suggest the populaton…Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the given level of significance α using the given sample statistics. Assume the sample statistics are from independent random samples. Claim: p1=p2, α=0.10 Sample statistics: x1=142, n1=156 and x2=144, n2=188 Find the standardized test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Use the following sample to evaluate H0: μ = 65, at significance level α = 0.05. 53 75 68 53 57 12 4 10 45 94 23 73 9 41 79 92 90 46 49 71 State the correct test and your conclusion. T-test. Reject Ho. T-test. Fail to reject Ho. Z-test. Fail to reject Ho. Z-test. Reject Ho.
