Use the Following Information to Answer the Question $\mathrm { H } _ { 0 } : \mathrm { p } = 0.6$

Essay

Use the following information to answer the question. A health foods shop owner is wondering if his customer's dailyvitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a newsreport that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have agreater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null andalternative hypothesis:
H0:
p=0.6 and Ha:
p>0.6. The shop owner collected data from 50 randomly selected customers.
-To continue the study, the shop owner decides to collect data from 60 customers between the ages of 22 and 27 to see whether the proportion in this age group is different from the general population of adults. From this sample, 26 reported that they took a daily vitamin. The null hypothesis for this test is $\mathrm { H } _ { 0 } : \mathrm { p } = 0.6$ . and the alternative hypothesis is $: \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.6$ . Assume that the conditions that must be met in order for us to use the $N ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\hat { p }$ , the observed test statistic, and the p-value associated with this observed value. Round all values to the nearest thousandth.