3)The telephone company surveys its customers to see how many would like even mo

Question

3)The telephone company surveys its customers to see how many would like even more expanded services, like call forwarding to your cell phone, linked voice mail systems, etc. Out of 255 customers surveyed, 137 of them were in favor of expanded service. The company president will implement this plan if there is over 50% in favor of expanded service. What is the test statistic for this hypothesis test?

4)45% of Americans are Democrats, according the Democratic party. After some political upheaval in Congress, a survey was taken to determine if there was a change the number of Democrats in the country. What type of test is this?

Question 4 options:

Left tailed

Right tailed

Two tailed

5)According to a past survey, 23% of Americans have hypertension. After a stringent regimen of diet and exercise, 75 people were then tested and 18 were found to have hypertension. Based on this sample, does diet and exercise reduce hypertension? Use a significance level of 0.05.

Question 5 options:

No

Yes

Explanation / Answer

3)The telephone company surveys its customers to see how many would like even more expanded services, like call forwarding to your cell phone, linked voice mail systems, etc. Out of 255 customers surveyed, 137 of them were in favor of expanded service. The company president will implement this plan if there is over 50% in favor of expanded service. What is the test statistic for this hypothesis test?

4)45% of Americans are Democrats, according the Democratic party. After some political upheaval in Congress, a survey was taken to determine if there was a change the number of Democrats in the country. What type of test is this?

Left tailed

Right tailed

Two tailed

If we have Null hypothesis, H0 : 1 0

And Alternate hypothesis, H1: 1 0, where a difference is hypothesized then this is called a two-tailed test.

5)According to a past survey, 23% of Americans have hypertension. After a stringent regimen of diet and exercise, 75 people were then tested and 18 were found to have hypertension. Based on this sample, does diet and exercise reduce hypertension? Use a significance level of 0.05.

No

Yes

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

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

Null hypothesis: P = 0.23
Alternative hypothesis: P < 0.23

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, is a one-sample z-test.

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

= sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.23 * 0.77) / 75] = 0.04859
z = (p - P) / = (0.24 - 0.23)/0.04859 = 0.2058

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 less than 0.2058. We use the Normal Distribution Calculator to find P(z < 0.2058)

The P-Value is 0.418474.
The result is not significant at p < 0.05.

Interpret results. Since the P-value (0.418474) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Fail to reject null hypothesis. That is, we have insufficient evidence to claim that  diet and exercise reduce hypertension.

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