91Ó°ÊÓ

Describe the main characteristics of an \(F\) distribution.

Find the critical value of \(F\) for an \(F\) distribution with \(d f=\) \((3,12)\) and a. area in the right tail \(=.05\) b. area in the right tail \(=.10\)

A consumer agency wanted to find out if the mean time taken by each of three brands of medicines to provide relief from a headache is the same. The first drug was administered to six randomly selected patients, the second to four randomly selected patients, and the third to five randomly selected patients. The following table gives the time (in minutes) taken by each patient to get relief from a headache after taking the medicine. $$ \begin{array}{ccc} \hline \text { Drug I } & \text { Drug II } & \text { Drug III } \\ \hline 25 & 15 & 44 \\ 38 & 21 & 39 \\ 42 & 19 & 54 \\ 65 & 25 & 58 \\ 47 & & 73 \\ 52 & & \\ \hline \end{array} $$ At a \(2.5 \%\) significance level, will you reject the null hypothesis that the mean time taken to provide relief from a headache is the same for each of the three drugs?

A farmer wants to test three brands of weight-gain diets for chickens to determine if the mean weight gain for each of these brands is the same. He selected 15 chickens and randomly put each of them on one of these three brands of diet. The following table lists the weights (in pounds) gained by these chickens after a period of 1 month. $$ \begin{array}{ccc} \hline \text { Brand A } & \text { Brand B } & \text { Brand C } \\ \hline .8 & .6 & 1.2 \\ 1.3 & 1.3 & .8 \\ 1.7 & .6 & .7 \\ .9 & .4 & 1.5 \\ .6 & .7 & .9 \\ \hline \end{array} $$ a. At a \(1 \%\) significance level, can you reject the null hypothesis that the mean weight gain for all chickens is the same for each of these three diets? b. If you did not reject the null hypothesis in part a, explain the Type II error that you may have made in this case. Note that you cannot calculate the probability of committing a Type II error without additional information.