Question

In​ 1997, a survey of 880 households showed that 149 of them use​ e-mail. Use those sample results to test the claim that more than​ 15% of households use​ e-mail. Use a 0.05 significance level. Use this information to answer the following questions.

b. What is the test​ statistic?

Z=

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

c. What is the​ P-value?

​P-value=

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

d. What is the​ conclusion?

There is sufficient evidence to support the claim that more than​ 15% of households use​ e-mail.

There is not sufficient evidence to support the claim that more than​ 15% of households use​ e-mail.

e. Is the conclusion valid​ today? Why or why​ not?

a.Yes, the conclusion is valid today because the requirements to perform the test are satisfied.

​b.No, the conclusion is not valid today because the population characteristics of the use of​ e-mail are changing rapidly.

c.You can make no decisions about the validity of the conclusion today.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.15

H_a : p > 0.15

= x / n = 149 / 880 = 0.1693

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1693 - 0.15 / [(0.15 * 0.85) / 880]

= 1.605

= 1.61

P(z > 1.61) = 1 - P(z < 1.61) = 0.0537

P-value = 0.054

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim that more than​ 15% of households use​ e-mail.

b. No, the conclusion is not valid today because the population characteristics of the use of​ e-mail are changing rapidly