Question

A poll of a random sample of 2570 people found that 70​% said that religion is at least​ "somewhat important" in their lives. The screenshot to the right shows how a calculator reports the results of a significance test for which the alternative hypothesis is that a majority of people believe religion is at least​ "somewhat important" in their lives. State and interpret the five steps of a significance test in this​ context, using the information shown in the screenshot to provide the particular values for the​ hypothesis, test​ statistic, and​ P-value.

1-PropZTest

prop> 0.50, z=20.28, p=1.09e-91, Sample proporiton=.70, n=2570

a.) Is the response a categorical variable, with a defined population proportion?

1.Yes

2.No

b.) Is n large enough to expect at least 15 successes and 15 failures?

c.) State the null hypothesis

1. p<0.50

2. p=0.50

3. p does not equal 0.50

4. p>0.50

d.) State the alternative hypothesis:

1. p=0.50

2. p does not equal 0.50

3. p<0.50

4. p>0.50

e.) The sample proportion for n=2570 is 0.70.

Find the test static, z=

f.) Find the P-value

1. P-Value =0.1

2. P-value =0.05

3. P-value≈​0

4. P-value≈​1

g.) Make a conclusion

1.Since the ​P-value≈​0, the sample supports the alternative hypothesis. There is very strong evidence that a majority of people believe that religion is at least​ "somewhat important" in their lives.

2. Since the ​P-value≈​1, the sample supports the null hypothesis. There is very strong evidence that a majority of people do not believe that religion is at least​ "somewhat important" in their lives.

Answer 1

(a) Yes, the response religion is somewhat important is a categorical variable

(b) Yes number of successes = 0.7 * 2570 = 1799 and 0.3 * 2570 = 771 are both greater than 15

(c) The null Hypothesis: p = 0.5

(d) The Alternative Hypothesis: p > 0.5

(e) The sample proportion is 0.7

The Test Statistic

(f) The p value

(f) The p value right tail = 0.0000

(g) Since p value is 0, the sample supports the alternative hypothesis. There is very strong evidence that a majority of people believe that religion is at least 'somewhat important' in their lives..