I need help finding the p-value. Also, could you add how you got the answer so I can better understand it. Thank you!

Unit 4, Topic 17, Exercise 17-20

Smoking in the Military

In July of 2009, health experts urged the U.S. military to ban smoking, even though smoking has long been associated with military service. The Centers for Disease Control and Prevention estimate that 20.9 % of American adults smoke.

a. Define the relevant parameter for testing whether American soldiers are more likely to smoke than American adults in general.

*The parameter is, the proportion of all American soldiers who smoke.

b. State the appropriate null and alternative hypotheses, in symbols and in words.

*The null hypothesis is that the proportion of all American soldiers who smoke is 0.209. In symbols, Upper H Subscript 0 Baseline colon pi equals 0.209. The alternative hypothesis is that the proportion of all American soldiers who smoke is greater than 0.209. In symbols, Upper H Subscript a Baseline colon pi greater-than 0.209.

An article in USA Today (Zoroya, 2009) reported that 37 % of U.S. soldiers smoke, but the article did not mention a sample size on which this statistic was based. For now suppose that the sample size was 200.

c. Are the technical conditions for the z-statistic satisfied? Yes

d. Calculate the test statistic and p-value.

Round the test statistic to two decimal places and the p-value to four decimal places.

z= 5.5998

p-value= _______________

e. State the test decision at the 0.06 level, and summarize your conclusion about whether American soldiers are more likely to smoke than Americans in general.

*Reject Upper H0. There is very strong evidence that the proportion of American soldiers who smoke is greater than the proportion of American adults who smoke.

f. If the sample actually involves more than 200 soldiers, would the sample data be statistically significant at the 0.06 level? Explain how you know.

*For a sample size larger than 200, the value of the test statistic would increase, resulting in a smaller p-value. Thus, the data would be statistically significant at the 0.06 level.

Same with this, please add the how the answer was gotten to better understand it. Thank you!

Unit 4, Topic 18, Exercise 18-28

Pop vs. Soda

The pop-vs.-soda website (popvssoda.com) asked people visiting the site to vote for their preferred name for a generic cola drink: pop, soda, coke, other. A total of 293,772 responses were received from the United States, of which 108,707 answered "pop", 120,130 answered "soda", 46,883 answered "coke", and 18,052 answered "other".

a. Determine a 99.9 % confidence interval for the population proportion who would answer "pop".

Round your answers to three decimal places. (_______________,_________________)

b. Based only on the confidence interval in part a, what can you say about the p-value for a significance test of whether the population proportion who would answer "pop" differs from 0.4? Explain your answer.

• Based on this confidence interval, you know the p-value for a two-sided significance test of Upper H Subscript 0 Baseline colon pi equals 0.4 would be greater than 0.001 because the value 0.4 is in this 99.9 % confidence interval.
• Based on this confidence interval, you know the p-value for a two-sided significance test of Upper H Subscript 0 Baseline colon pi equals 0.4 would be equal to 0.001 because the value 0.4 is not in this 99.9 % confidence interval.
• Based on this confidence interval, you know the p-value for a two-sided significance test of Upper H Subscript 0 Baseline colon pi equals 0.4 would be less than 0.001 because the value 0.4 is not in this 99.9 % confidence interval.
• Based on this confidence interval, you know the p-value for a two-sided significance test of Upper H Subscript 0 Baseline colon pi equals 0.4 would be equal to 0.001 because the value 0.4 is in this 99.9 % confidence interval.

c. Explain why the confidence interval in part a is so narrow, despite a very high confidence level.

• The confidence interval found in part a is so narrow because the sample size is so large. This makes the margin-of-error very small.
• The confidence interval found in part a is so narrow because the population proportion is close to 0.5. This makes the margin-of-error very small.
• The confidence interval found in part a is so narrow because the sample size is so large. This makes the margin-of-error very large.

d. Does the very large sample size in this study ensure that the sample is likely to be representative of the population? Explain.

• No, the large sample does not ensure the sample will be representative of the population. The only way to ensure a representative sample is to use an unbiased sampling method, such as simple random sampling.
• Yes, the large sample does ensure the sample will be representative of the population