Question

Use the following information to answer questions 5 through 7. A health foods shop owner is wondering if his customer's daily vitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion of adults who take a daily vitamin.

5) (4 points) State the null hypothesis and the alternate hypothesis in this study.

6) (5 points) 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. Assume that the conditions that must be met in order for us to use the appropriate statistical test.

Find the values of the sample proportion, p^, the observed test statistic, and the p-value associated with this observed value. Round all values to the nearest thousandth.

7) (3 points) Based on a 5% significance level, write a conclusion by interpreting the p-value. Be sure to clearly state the decision regarding the null hypothesis.

Answer 1

Thank you.

Solutions 6 from the given Information. Here, het p= true proportion of all adults reported that they took a daily vitamina Nell hypothesis, Hosp20.60 vs. Alternative hypothesis, Hup< 0.60 6 Here, P = 26/60=0.43 observed Test statistic=2.8 -0.60 10.60x0.40 - 2.64 V 60 p-value = p (2<-2.4 | 2 ~N(0,1) =) 0.00 Here, since the p-value is <0.05, so we can reject Ho at 5% level of significance and here, conclude that there is insufficient evidence to accept the claims of news report and the shop owner.