Question

Small-business telephone users were surveyed 6 months after access to carriers other than Carrier A became available for​ wide-area telephone service. Of a random sample of 230 Carrier A​ users, 160 said they were attempting to learn more about their​ options, as did 229 of an independent random sample of 270 users of alternate carriers.​ Test, at the 1% significance level against a​ two-sided alternative, the null hypothesis that the two population proportions are the same.

Let Px be the proportion of Carrier A users who said they were attempting to learn more about their options and Py be the proportion of users of alternate carriers who said they were attempting to learn more about their options. Determine the null and alternative hypotheses. Choose the correct answer below.

A. H0​: Px−Py=0

H1​: Px −py ≥ 0

B. H0​: Px−Py =0

H1​: Px−Py >0

C. H0​: Px−Py = 0

H1​: Px−Py < 0

D. H0​: Px−Py = 0

H1: Px−Py ≤ 0

E. H0​: Px−Py ≠ 0

H1​: Px−Py = 0

F. H0​: Px−Py =0

H1​: Px−Py ≠ 0

The test statistic is Z =______________

The critical​ value(s) is(are)__________

Since the test statistic is less or greater ??? than the critical​ value(s), reject or not reject H0 ??

there is sufficient or insufficient ????? evidence to conclude that there is a difference between the two population proportions.

Answer 1

Testing the null hypothesis that the two population proportions are the same.

F. H0​: Px−Py =0

H1​: Px−Py ≠ 0

use TI 84 calculator

STAT --> TESTS --> 2-PropZtest

x1 :160 , n1:230 , x2:229 , n2: 270

p1 ≠ p2

Press calculate, result is test statistic z = -4.09 (2 decimals)

Critical z value = -2.58 and 2.58 [From z critical value table with alpha = 0.01/2] (2 decimals)

We can see that the z test statistic < -2.58, we can reject the null hypothesis

Since the test statistic is less than the critical​ value(s) -2.58, reject reject H0.

there is sufficient evidence to conclude that there is a difference between the two population proportions.