To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "blue collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is $\mathrm { H } _ { 0 } : \mathrm { p } = 0.26$ and the alternative hypothesis is $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } 0.26$. The researcher collected data from a random sample of 90 adults with "blue collar" jobs of which 30 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the $\mathrm { N } ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\hat { p }$, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth.
A) $\hat { \mathrm { p } } = 0.333 , \mathrm { z } = 1.586 , \mathrm { p }$-value $= 0.056$
B) $\hat { \mathrm { p } } = 0.289 , \mathrm { z } = - 0.829$, p-value $= 0.407$
C) $\hat { p } = 0.667 , z = 8.795 , p$-value $= 0.000 ^ { + }$
D) $\hat { p } = 0.333 , \mathrm { z } = 0.067 , \mathrm { p }$-value $= 0.946$

Question

To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "blue collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is $\mathrm { H } _ { 0 } : \mathrm { p } = 0.26$ and the alternative hypothesis is $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.26$. The researcher collected data from a random sample of 90 adults with "blue collar" jobs of which 30 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the $\mathrm { N } ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\hat { p }$, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth.
A) $\hat { \mathrm { p } } = 0.333 , \mathrm { z } = 1.586 , \mathrm { p }$-value $= 0.056$
B) $\hat { \mathrm { p } } = 0.289 , \mathrm { z } = - 0.829$, p-value $= 0.407$
C) $\hat { p } = 0.667 , z = 8.795 , p$-value $= 0.000 ^ { + }$
D) $\hat { p } = 0.333 , \mathrm { z } = 0.067 , \mathrm { p }$-value $= 0.946$

Quizplus · Accepted Answer

The sample proportion $\hat{p}$ is calculated as 30/90 = 0.333. The test statistic $z$ is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $p_0 = 0.26$ and $n = 90$. This gives $z = 1.586$. The p-value for a one-tailed test with $z = 1.586$ is approximately 0.056.

To Continue the Study into the Drinking Habits of Adults H0:p=0.26\mathrm { H } _ { 0 } : \mathrm { p } = 0.26H0​:p=0.26

To Continue the Study into the Drinking Habits of Adults $\mathrm { H } _ { 0 } : \mathrm { p } = 0.26$