Question

2.) Assume that you have a sample of n1 = 8​, with the sample mean X overbar 1= 42​, and a sample standard deviation of S1 = 4​, and you have an independent sample of n2=15 from another population with a sample mean of X overbear 2 = 34 and a sample standard deviation of S2 = 5.

What assumptions about the two populations are necessary in order to perform the​ pooled-variance t test for the hypothesis H0: μ1=μ2 against the alternative H1: μ1>μ2 and make a statistical​ decision?

Choose the correct answer below.

A.It is necessary to assume that the populations from which you are sampling have equal population means and positive standard deviations.

B.It is necessary to assume that the populations from which you are sampling have negative t Subscript STATtSTAT test statistics and unequal sample means.

C. It is necessary to assume that the populations from which you are sampling have independent normal distributions and equal variances.

D. It is necessary to assume that the populations from which you are sampling have unequal variances and equal sizes.

3.) Assume that you have a sample of n1 = 8​, with the sample mean X overbar 1= 47​, and a sample standard deviation of S1 = 7​, and you have an independent sample of n2 = 14 from another population with a sample mean of X2 = 35​, and the sample standard deviation S2 = 6. Construct a 95​% confidence interval estimate of the population mean difference between μ1 and μ2.

____ ≤ μ1−μ2 ≤ ____

​(Type an integer or decimal rounded to two decimal places as​ needed.)

11.) The following information is available for two samples drawn from independent normally distributed populations.

Population A	n = 21	S2 = 184.5
Population B	n = 21	S2 = 157.7

What is the upper critical value for F if the level of​ significance, α, is 0.1 and the alternative hypothesis is H1: σ 2/1 ≠ σ 2/2?

The upper critical value for F is ______.

​(Round to two decimal places as​ needed.)

Answer 1

2) Option - C) It is necessary to assume that the populations from which you are sampling have independent normal distributions and equal variances.

3)

              

            

At 95% confidence level, the critical value is t^* = 2.179

The 95% confidence interval is

() +/- t^* * sqrt(s1^2/n1 + s2^2/n2)

= (47 - 35) +/- 2.179 * sqrt(7^2/8 + 6^2/14)

= 12 +/- 6.43

= 5.57, 18.43

11) At = 0.1, the upper critical value is F_R = F(0.05, 20, 20) = 2.12