The heights of 12 randomly selected adult female golden retreivers are given below (in inches). The sign test at the 0.1 significance level will be used to test the claim that the population median is greater than 21 inches.
\begin{tabular}{|r|r|}
\hline 22.4 & 22.4 \\
\hline 22 & 23.2 \\
\hline 23.3 & 20.5 \\
\hline 21 & 22 \\
\hline 22.5 & 23.3 \\
\hline 21 & 21 \\
\hline
\end{tabular}
(a) What is the value of the test statistic used in this sign test?
8
(b) What is the critical value in this sign test?
8
(c) What is the correct conclusion of this sign test?
There is sufficient evidence to support the claim that the population median is greater than 21 inches.

There is not sufficient evidence to warrant rejection of the claim that the population median is greater than 21 inches.
There is sufficient evidence to warrant rejection of the claim that the population median is greater than 21 inches.

There is not sufficient evidence to support the claim that the population median is greater than 21 inches.

Step 1 ：The given heights of 12 randomly selected adult female golden retrievers are 22.4, 22.4, 22, 23.2, 23.3, 20.5, 21, 22, 22.5, 23.3, 21, and 21 inches.

Step 2 ：We are testing the claim that the population median is greater than 21 inches using the sign test.

Step 3 ：To calculate the test statistic, we count the number of observations that are greater than the hypothesized median (21 inches). The test statistic is \(8\).

Step 4 ：The critical value for the sign test can be found in the binomial distribution table for n=12 (number of observations) and α=0.1 (significance level). The critical value is \(8\).

Step 5 ：We compare the test statistic and the critical value. If the test statistic is greater than or equal to the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population median is greater than 21 inches.

Step 6 ：In this case, the test statistic (\(8\)) is equal to the critical value (\(8\)), so there is sufficient evidence to support the claim that the population median is greater than 21 inches.

Step 7 ：Final Answer: The value of the test statistic used in this sign test is \(\boxed{8}\). The critical value in this sign test is \(\boxed{8}\). There is sufficient evidence to support the claim that the population median is greater than 21 inches.