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Given information, Significance level α=0.05 Sample size n1=18 Sample size n2=20 Confidence interval CI=45.6, 56.7(a) The confidence interval is calculated as, CI=x¯1-x¯2-t0.025, df*sp1n1+1n2, x¯1-x¯2+t0.025, df*sp1n1+1n2 The difference between the upper and the lower confidence levels will give the margin of error. It will be calculated as, x¯1-x¯2+t0.025, df*sp1n1+1n2-x¯1-x¯2-t0.025, df*sp1n1+1n2=56.7-45.62*t0.025, df*sp1n1+1n2=11.1t0.025, df*sp1n1+1n2=5.55 The difference between observed means x¯1-x¯2 is the sum of lower confidence interval and the margin of error or is the difference between the lower confidence interval and the margin of error. The difference between observed means x¯1-x¯2 will be calculated as follows: x¯1-x¯2-t0.025, df*sp1n1+1n2=45.6x¯1-x¯2=45.6+t0.025, df*sp1n1+1n2=45.6+5.55=51.15(b) The degrees of freedom can be calculated as follows: df=n1+n2-2=18+20-2=36 The margin of error obtained for 95% confidence interval is, MOE=t0.025, 36*sp1n1+1n2=5.55 Therefore, sp1n1+1n2=MOEt0.025, 36=5.552.028=2.7367 The critical value for 99% confidence level, with 36 degrees of freedom, t0.005, 36=±2.719. The margin of error for 99% confidence interval will be calculated as: MOE=t0.005, 36*sp1n1+1n2=2.719*2.7367=7.441 (c) (i) The answer is can't say. The 95% confidence interval interpretation is that there is only 95% confidence that the difference between the two population mean is between the confidence interval (45.6, 56.7). So, it cannot be determined whether it is included in the 95% confidence interval or not. (ii) The answer is yes. The 95% confidence interval is calculated based on the difference between the two sample means. Therefore, it is included in the 95% confidence interval. (iii) The answer is yes. It is because the interpretation of 95% confidence interval is that there is 95% probability that the difference between the two population mean is between the confidence interval (45.6, 56.7). (iv) The answer is no. The larger the sample size will be, the lesser the margin of error will become. It will reduce the width of the confidence interval. Therefore, the confidence interval will not include more values for the difference between the two population means.

Math

Statistics

Question: A 95% confidence interval (using the conservative value for the degrees of freedom) for H1-2, based on two independent samples of sizes 18 and 20, respectively, gives us (45.6, 56.7). (a) What was the observed difference between the two sample means and f? (b) What would be the margin of error for a 99% confidence interval for u - us? (c) Answer each of the following questions with yes, no, or can't tell. i. Is the difference between the two population means, H1-2, included in the 95% confidence interval? ii. Is the difference between the two sample means, - 2, included in the 95% confidence interval? iii. Is the probability that the difference between the two population means, pi- Hz, falls between 45.6 and 56.7 equal to 0.95? 1 iv. If larger samples were used to calculate the confidence interval, would it include more values for the difference between the two population means?

Question: A 95% confidence interval (using the conservative value for the degrees of freedom) for H1-2, based on two independent samples of sizes 18 and 20, respectively, gives us (45.6, 56.7). (a) What was the observed difference between the two sample means and f? (b) What would be the margin of error for a 99% confidence interval for u - us? (c) Answer each of the following questions with yes, no, or can't tell. i. Is the difference between the two population means, H1-2, included in the 95% confidence interval? ii. Is the difference between the two sample means, - 2, included in the 95% confidence interval? iii. Is the probability that the difference between the two population means, pi- Hz, falls between 45.6 and 56.7 equal to 0.95? 1 iv. If larger samples were used to calculate the confidence interval, would it include more values for the difference between the two population means?

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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