Question

(2 points) In order to compare the means of two populations, independent random samples of 49 observations are selected from each population, with the following results: Sample 1 Sample 2 x = 1 *2 = 3 S = 195 140 s2 = (a) Use a 97 % confidence interval to estimate the difference between the population means (41 - H2). ( 4- 42) (b) Test the null hypothesis: H :(#1 - 12) = 0 versus the alternative hypothesis: H, :( - M2) 0. Using a = 0.03, give the following: 0 the test statistic z = (1) the positive critical z score (H) the negative critical z score The final conclustion is A. We can reject the null hypothesis that (H1-H2) = 0 and accept that (#1 - 2) *0. B. There is not sufficient evidence to reject the null hypothesis that (41 - M2) = 0. (©) Test the null hypothesis: H. : CH1 - H2) = 22 versus the alternative hypothesis: H : (H1 - H2) # 22. Using a = 0.03. give the following: 0 the test statistic z = () the positive critical z score (HD the negative critical z score The final conclustion is Al want the hathaole that 22 and arrant that 22

Answer 1

using excel

we have

Z Test for Differences in Two Means
Data
Hypothesized Difference	0
Level of Significance	0.03
Population 1 Sample
Sample Size	49
Sample Mean	1
Population Standard Deviation	140			97% confidence interval
Population 2 Sample
Sample Size	49		margin of error	74.41924
Sample Mean	3
Population Standard Deviation	195		lower limit	-76.4192
			upper limit	72.41924
Intermediate Calculations
Difference in Sample Means	-2
Standard Error of the Difference in Means	34.2932
Z Test Statistic	-0.0583
Two-Tail Test
Lower Critical Value	-2.1701
Upper Critical Value	2.1701
p-Value	0.9535
Do not reject the null hypothesis

a ) 97% confidence interval is

-76.4192 <u1-u2<72.4192

b ) i) the test stat z =-0.0583

ii) positive critical value = 2.1701

iii) negative critical value =-2.1701

conclusion is given by option B

c ) using excel

we have

Z Test for Differences in Two Means
Data
Hypothesized Difference	22
Level of Significance	0.03
Population 1 Sample
Sample Size	49
Sample Mean	1
Population Standard Deviation	140
Population 2 Sample
Sample Size	49
Sample Mean	3
Population Standard Deviation	195
Intermediate Calculations
Difference in Sample Means	-2
Standard Error of the Difference in Means	34.2932
Z Test Statistic	-0.6998
Two-Tail Test
Lower Critical Value	-2.1701
Upper Critical Value	2.1701
p-Value	0.4840
Do not reject the null hypothesis

i) the test stat z =-0.6998

ii) positive critical value = 2.1701

iii) negative critical value =-2.1701

conclusion is given by option B