The heights of 12 randomly selected men are given below (in inches). The sign test at the 0.025 significance level will be used to test the claim that the population median is greater than 70 inches.
\begin{tabular}{|r|r|}
\hline 71.6 & 71 \\
\hline 71.7 & 69.4 \\
\hline 71.7 & 72.5 \\
\hline 67.8 & 70 \\
\hline 7.0 & 72.9 \\
\hline 72.1 & 70 \\
\hline
\end{tabular}
(a) What is the value of the test statistic used in this sign test?
(b) What is the critical value in this sign test?
(c) What is the correct conclusion of this sign test?
There is sufficient evidence to warrant rejection of the claim that the population median is greater than 70 inches.
There is not sufficient evidence to warrant rejection of the claim that the population median is greater than 70 inches.

There is sufficient evidence to support the claim that the population median is greater than 70 inches.
There is not sufficient evidence to support the claim that the population median is greater than 70 inches.

Step 1 ：We are given the heights of 12 randomly selected men and we are to test the claim that the population median is greater than 70 inches. The null hypothesis (H0) is that the median is equal to 70 inches, and the alternative hypothesis (H1) is that the median is greater than 70 inches.

Step 2 ：The test statistic for the sign test is the number of positive signs, i.e., the number of observations greater than the hypothesized median. Counting the number of heights that are greater than 70 inches, we get a test statistic of \(\boxed{7}\).

Step 3 ：The critical value for a one-tailed sign test can be found using the binomial distribution. The critical value is the smallest number of successes such that the probability of getting that many successes or more is less than the significance level. Using the binomial distribution function, we find that the critical value is \(\boxed{3}\).

Step 4 ：To make a conclusion, we compare the test statistic to the critical value. If the test statistic is greater than 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 70 inches. If the test statistic is less than or equal to the critical value, we do not reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the population median is greater than 70 inches.

Step 5 ：In this case, the test statistic (7) is greater than the critical value (3), so we reject the null hypothesis. Therefore, there is \(\boxed{\text{sufficient evidence to warrant rejection of the claim that the population median is greater than 70 inches}}\).