Problem
Question 1, 7.3.3
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Find the critical value(s) and rejection region(s) for the indicated $t$-test, level of significance $\alpha$, and sample size $n$. Left-tailed test, $\alpha=0.10, \mathrm{n}=17$
Click the icon to view the $t$-distribution table.
The critical value(s) is/are -1.337 .
(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)
Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to the nearest thousandth as needed.)
A. $\mathrm{t}>\square$
B. $\square\square$
D. $t<\square$
Solution
Step 1 ：Given values are level of significance \(\alpha = 0.10\) and sample size \(n = 17\).
Step 2 ：Calculate the degrees of freedom as \(df = n - 1 = 17 - 1 = 16\).
Step 3 ：Find the critical value using the t-distribution table. The critical value is the value beyond which we would reject the null hypothesis in a left-tailed t-test.
Step 4 ：The critical value is approximately \(-1.337\).
Step 5 ：The rejection region for a left-tailed test is all values less than the critical value.
Step 6 ：So, the rejection region is all values less than \(-1.337\).
Step 7 ：Final Answer: The critical value is \(\boxed{-1.337}\). The rejection region is \(t<\boxed{-1.337}\).
