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41 votes
Find the P-value for the indicated hypothesis test.

A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.

A. 0.1271
B. 0.2542
C. 0.1401
D. 0.2802

User Cdosborn
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3.3k points

2 Answers

27 votes
27 votes

Final answer:

The p-value for a hypothesis test regarding the proportion of forty-year-old smokers cannot be determined with the given information and without the exact calculation details. A statistical software or calculator would be typically used after forming the null and alternative hypotheses and ensuring that the conditions for a normal approximation are met.

Step-by-step explanation:

To find the p-value for the hypothesis test, we have to consider the following: A sample of 139 forty-year-old men contains 26% smokers, and we want to test the claim that the percentage of forty-year-old men who smoke is 22%. This is a test for a single population proportion.

We start by formulating our null hypothesis (H0: p = 0.22) and alternative hypothesis (Ha: p ≠ 0.22) assuming a two-tailed test since no direction is specified. We then calculate the test statistic using the formula for a sample proportion, which follows a normal distribution because np and n(1-p) are both greater than 5. However, the exact calculation for the test statistic and the p-value is not provided here. The closest possible p-value given the options would be a judgment based on standard statistical methods.

Based on typical output from a statistical software or a calculator, we can take an educated guess. Without the calculation details, the correct p-value for this scenario cannot be determined from the information given. However, when analyzing statistical results, the p-value is compared to the level of significance (α) to make a decision about the null hypothesis. If the p-value is less than α, typically 0.05, the null hypothesis is rejected. If it is greater, we fail to reject the null hypothesis.

User Pandith Padaya
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3.8k points
14 votes
14 votes
First identify the following
Population mean: 22%
Sample size = 139
Sample mean: 26%
Z = (sample mean - population mean)/sqrt((pop mean*(1-pop mean))/sample size

Z = 0.04/sqrt((0.22)(0.78))/139
Z= 1.1384
P value using z score table is 0.8729
But that is for values within that range we want values greater than 22%. So it would be 1-0.8729 = 0.1271 or A
User Ismael Miguel
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2.9k points