To test Hg: u= 60 versus H,: u< 60, a random sample of size n=26 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. E Click here to view the t-Distribution Area in Right Tail. (a) If x= 57.4 and s= 10.7, compute the test statistic. t, = (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.05 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given. Critical Value: (Round to three decimal places. Use a comma to separate answers as needed.) (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below.

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The image is a statistical table titled "Area in Right Tail" which presents critical values for the t-distribution based on specific degrees of freedom (df) and tail probabilities (α). 

**Table Columns:**
- The header row defines different levels of significance (α) from 0.25 to 0.0005.

**Table Rows:**
- The first column lists degrees of freedom (df) from 1 to 100.
- Each subsequent column corresponds to a right-tail probability value (α) and presents the critical value for that specific combination of degrees of freedom and tail probability.

**Explanation:**
- Each cell in the table provides the t-value that marks the cutoff for the specified area under the right tail of the t-distribution, given the degrees of freedom and significance level.

This table is used in hypothesis testing and confidence interval calculations, helping determine critical t-values for one-tailed tests.
Transcribed Image Text:The image is a statistical table titled "Area in Right Tail" which presents critical values for the t-distribution based on specific degrees of freedom (df) and tail probabilities (α). **Table Columns:** - The header row defines different levels of significance (α) from 0.25 to 0.0005. **Table Rows:** - The first column lists degrees of freedom (df) from 1 to 100. - Each subsequent column corresponds to a right-tail probability value (α) and presents the critical value for that specific combination of degrees of freedom and tail probability. **Explanation:** - Each cell in the table provides the t-value that marks the cutoff for the specified area under the right tail of the t-distribution, given the degrees of freedom and significance level. This table is used in hypothesis testing and confidence interval calculations, helping determine critical t-values for one-tailed tests.
To test \( H_0: \mu = 60 \) versus \( H_1: \mu < 60 \), a random sample of size \( n = 26 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.

Click here to view the t-Distribution Area in Right Tail.

**(a)** If \( \bar{x} = 57.4 \) and \( s = 10.7 \), compute the test statistic.

\( t_0 = \) (Round to three decimal places as needed.)

**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.

Critical Value:  \_\_\_  (Round to three decimal places. Use a comma to separate answers as needed.)

**(c)** Draw a t-distribution that depicts the critical region. Choose the correct answer below.

- **Option A:** A graph showing a left-tailed distribution with the critical region shaded on the left.
- **Option B:** A graph showing a two-tailed distribution with critical regions shaded on both tails.
- **Option C:** A graph showing a right-tailed distribution with the critical region shaded on the right.

**(d)** Will the researcher reject the null hypothesis?

- \(\square\) No, because the test statistic falls in the critical region.
- \(\square\) Yes, because the test statistic does not fall in the critical region.
- \(\square\) Yes, because the test statistic falls in the critical region.
- \(\square\) No, because the test statistic does not fall in the critical region.
Transcribed Image Text:To test \( H_0: \mu = 60 \) versus \( H_1: \mu < 60 \), a random sample of size \( n = 26 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. Click here to view the t-Distribution Area in Right Tail. **(a)** If \( \bar{x} = 57.4 \) and \( s = 10.7 \), compute the test statistic. \( t_0 = \) (Round to three decimal places as needed.) **(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.05 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given. Critical Value: \_\_\_ (Round to three decimal places. Use a comma to separate answers as needed.) **(c)** Draw a t-distribution that depicts the critical region. Choose the correct answer below. - **Option A:** A graph showing a left-tailed distribution with the critical region shaded on the left. - **Option B:** A graph showing a two-tailed distribution with critical regions shaded on both tails. - **Option C:** A graph showing a right-tailed distribution with the critical region shaded on the right. **(d)** Will the researcher reject the null hypothesis? - \(\square\) No, because the test statistic falls in the critical region. - \(\square\) Yes, because the test statistic does not fall in the critical region. - \(\square\) Yes, because the test statistic falls in the critical region. - \(\square\) No, because the test statistic does not fall in the critical region.
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