4.2.7: Let a random sample of size 17 from the normal distribution N(u, o²) yield = 4.7 and S2 = 5.76. Determine a 90% confidence interval for u.
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- 7.2.3 WP VS A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. Find the probability that a random sample of n = 6 fiber specimens will have sample mean tensile strength that exceeds 75.75 psi.Tests the claim that 1 <2. Assume the samples are random and independent. 01 = 0.65 ; 02 = 0.62 T = 46.77 ; E2 = 47.07 %3D n1 = 45; n2 = 33 a. Calculate the Standard Error o- = (3 decimal places) b. Calculate the Z-test statistic using the standard error from part a. z= (2 decimal places) C. At a = 0.07, Use the distribution table to find the critical values for the rejection region (3 decimal places) d. What is your conclusion? O Fail to reject the null hypothesis and do not support the claim O Accept the null hypothesis and support the claim O Accept the alternative hypothesis and reject the claim O Reject the null hypothesis and support the claim O Reject the alternative hypothesis and support the claimYou decide to play K number of video games, where K is a Poisson random variable with parameter A. Assume that time you spend on a video game k = 1, 2,..., K has a normal distribution with mean µg and variance of. Also assume that µk >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.
- Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = lB vs Ha : HA + HB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = p-value = i4.52 Random variables X and Y follow a joint distribution f(x, y) = = 2, 0< x≤y< 1, otherwise. 0, Determine the correlation coefficient between X and Y.Let X1,..., X100 ~ Bernoulli(p) be iid, where 02.2. Let Y₁, Y₂Yn denote a random sample from a gamma distribution with each Y-gamma (0; B) with known. Find a sufficient statistic for 8.Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA HB vs Ha : HA # µB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14.Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and MediaQ2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Осa) Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 2.6282.6681 is the standard deviation of the second sample. B) Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 4.15966.3763 is the standard deviation of the second sample.2.STATISTICAL INFERENCESEE MORE QUESTIONS
