Let X1, X2, X3, X4 and X5 constitute a random sample of size n=5 from a normaldistribution with o = 8. The null hypothesis H,: µ= 10 is to be rejected in favor ofthe alternative H;: µ # 10 when & <6 or x> 13.a. Find the probability of Type I error.b. Find the probability of Type II error if u = 15.c. Determine a critical region that has a = .05.d. Using the critical region in part c, sketch the power curve for u =7, 8, 9, 10, 11, 12, 13.%3D

Answered: Image /qna-images/answer/c26db634-2542-41fb-a009-207d57dc05b3.jpg

Answered: Let X1, X2, X3, X4 and X5 constitute a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 table to find the critical value(s) for the indicated alternative hypotheses, level of significance α, and sample sizes n1 and n2. Assume that the samples are independent, normal, and random. Ha: μ1≠μ2, α=0.20, n1=6, n2=8 Find the critical value(s) assuming that the population variances are equal
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 Media
Test the claim about the difference between two population means H, and u2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. Claim: 41 SH2; a = 0.10. Assume o, #o, Sample statistics: X, = 2417, s, = 179, n, = 12 and X2 = 2296, s2 = 53, n2 = 10 Identify the null and alternative hypotheses. Choose the correct answer below. 대= 내 : "H OF. Ho: H1 2H2 Find the standardized test statistic t. (Round to two decimal places as needed.) Find the P-value. (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. V Ho. There V enough evidence at the 10% level of significance to reject the claim.
Test the claim about the differences between two population variances at the given level of significance a using the given sample statistics. Assume that the sample statistics are from independent samples that are randomly selected and each population has a normal distribution. 1. Find the critical value. 2. Find the test statistic.
Give one method to increase statistical power and Which test statistic should you use if you are comparing two variances?
None
Assume that you have a sample of n, = 8, with the sample mean X, = 47, and a sample standard deviation of S, = 7, and you have an independent sample of n, = 7 from another population with a sample mean of X, = 37 and the sample standard deviation S, = 8. Assuming the population variances are equal, at the 0.01 level of significance, is there evidence that u, > H2? Determine the hypotheses. Choose the correct answer below. O A. Ho: H1 SH2 H1: Hy> H2 O B. Ho: H1 =H2 H: H1 # H2 O D. Ho: H1 H2 O C. Ho: H1> H2 H1: H1 SH2
Let X1 and X2 be independent standard normal random variables. Show that the joint distribution of Y, = a11X1+A12X2 + b1 Y2 = a2] X1 + A22X2+ b2 %3D is bivariate normal.
suppose the random variable X has a normal distribution with a mean of 10 and a variance of 256 calculate the following: P(12 < x < 20 ) USE DECIMAL VALUES AND ROUND OFF FINAL ANSWER TO TWO DECIMAL PLACES!
Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.
Plz help asap 46

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