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, $$ \alpha=0.025, n=17 $$ Click the icon to view the $$ t $$-distribution table. The critical value(s) is/are -2.120 . (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. $$ 1 $$ $$ \square $$ B. $$ \mathrm{t} $$ $$ \square $$ C. $$ \mathrm{t}

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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, $$ \alpha=0.025, n=17 $$ Click the icon to view the $$ t $$-distribution table. The critical value(s) is/are -2.120 . (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. $$ 1> $$ $$ \square $$ B. $$ \mathrm{t}< $$ $$ \square $$ and $$ \mathrm{t}> $$ $$ \square $$ C. $$ \mathrm{t}< $$ $$ \square $$ D. $$ \square $$ < $$ < $$ $$ \square $$

UpStudy AI · Accepted Answer

For a **left-tailed $$ t $$-test** with a significance level $$ \alpha = 0.025 $$ and sample size $$ n = 17 $$:

1. **Degrees of Freedom (df):**
   $$
   df = n - 1 = 17 - 1 = 16
   $$

2. **Critical Value:**
   Using the $$ t $$-distribution table for $$ df = 16 $$ and $$ \alpha = 0.025 $$ (since it's a left-tailed test), the critical value is:
   $$
   t_{\text{critical}} = -2.120
   $$
   *(Rounded to the nearest thousandth)*

3. **Rejection Region:**
   For a left-tailed test, the rejection region consists of all $$ t $$-values **less than** the critical value. Therefore:
   $$
   \text{Rejection Region: } t < -2.120
   $$

**Summary:**

- **Critical Value(s):** $$-2.120$$
- **Rejection Region:** $$ t < -2.120 $$

**Correct Choice:**

C. $$ \mathrm{t} < -2.120 $$
The critical value is -2.120, and the rejection region is $$ t < -2.120 $$.

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