Question

(1 point) In order to compare the means of two populations, independent random samples of 202 observations are selected from each population, with the following results: Sample 1 Sample 2 x1 = 4 x2 = 1 $1 = 105 s2 = 150 (a) Use a 90 % confidence interval to estimate the difference between the population means (41-42). < (41 - M2) (b) Test the null hypothesis: Ho : (41 - H2) = 0 versus the alternative hypothesis: H:(W1 - H2) 0. Using a = 0.1, give the following: the test statistic z = (ii) the positive critical z score (iii) the negative critical z score The final conclusion is A. We can reject the null hypothesis that (ui - H2) = 0 and accept that (M1-M2) * 0. B. There is not sufficient evidence to reject the null hypothesis that (U1 - H2) = 0. (c) Test the null hypothesis: H :( - ) = 29 versus the alternative hypothesis: H: (0 - My) # 29. Using a = 0.1, give the following: O the test statistic z = (ii) the positive critical z score (iii) the negative critical z score

Answer 1

The statistic software output for this problem is:

Two sample Z summary confidence interval: Hu: Mean of population 1 (Std. dev. = 105) H2 : Mean of population 2 (Std. dev. = 150) H1 - H2 : Difference between two means 90% confidence interval results: Difference ni n2 Sample mean Std. err. L. limit U. limit Hi-H2 202 202 3 12.882754 -18.190244 24.190244

(a)

-18.90 24.19

<μι – μ2 <

Two sample Z summary hypothesis test: Mi : Mean of population 1 (Std. dev. = 105) Hz: Mean of population 2 (Std. dev. = 150) - 2 : Difference between two means Ho : H1 - H2 = 0 HA : 1 - 2 0 Hypothesis test results: Difference ni n2 Sample mean Std. err. Z-stat P-value Hi - Hz 202 202 3 12.882754 0.23286947 0.8159

(b)

(i)

Test statistics = 0.2329

(ii)

Positive critical value = 1.645

(iii)

Negative critical value = -1.645

B. There is not sufficient evidence to reject the null hypothesis that (441 – 12) = 0).

(c)

Two sample Z summary hypothesis test: Hu: Mean of population 1 (Std. dev. = 105) H2 : Mean of population 2 (Std. dev. = 150) H1 - H2 : Difference between two means Ho : H1 - H2 = 29 HA: M1 - H229 Hypothesis test results: Difference ni n2 Sample mean Std. err. Z-stat H1 - H2 202 202 3 12.882754 -2.018202 P-value 0.0436

(i)

Test statistics = -2.0182

(ii)

Positive critical value = 1.645

(iii)

Negative critical value = -1.645