Question

In: Statistics and Probability

In? 1997, a survey of 840 households showed that 147 of them use? e-mail. Use those...

In? 1997, a survey of 840 households showed that 147 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.

a. Which of the following is the hypothesis test to be? conducted?

b. What is the test? statistic?

c. What is the? P-value?

d. What is the? conclusion?

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

or

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

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

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

Expert Solution

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.15
Alternative hypothesis: P > 0.15

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.01232
z = (p - P) / S.D

z = 2.03

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.03.

Thus, the P-value = 0.021

Interpret results. Since the P-value (0.021) is less than the significance level (0.05), we cannot accept the null hypothesis.

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

e) (B) Yes, the conclusion is valid today because the requirements to perform the test are satisfied.

orchestra answered 2 years ago

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