The U.S. Census Bureau claims that 26% of all U.S. businesses are owned by women. A researcher in Denver believes that the percent is higher there. A consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of them have female owners. What is the P value for testing the hypotheses H0:p=0.26 versus Ha:p>0.26 ?a) 0.946b) 0.172c) 0.344

Answer:b) 0.172Step-by-step explanation:We have a large sample size n = 410 and [tex]\hat{p} = 115/410 = 0.2805[/tex].  For testing the hypotheses [tex]H_{0}: p = 0.26[/tex] vs [tex]H_{1}: p > 0.26[/tex] (upper-tail alternative) the test statistic is given by [tex]Z = \frac{\hat{p}-0.26}{\sqrt{\hat{p}(1-\hat{p})/n}}[/tex] and the observed value is [tex]z_{0}=\frac{0.2805-0.26}{\sqrt{0.2805(1-0.2805)/410}}=0.924[/tex]. The p-value is computed as P(Z > 0.924) = 0.1777 where the random variable Z comes from a standard normal distribution.