If the researcher decides to test this hypothesis at the α=0.05 level of​ significance, determine the critical​ value(s). Although technology or a​ t-distribution table can

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(b) If the researcher decides to test this hypothesis at the α=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.

To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 22 \) 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 \( \overline{x} = 36.6 \) and \( s = 10.6 \), compute the test statistic.

\[
t_0 = -1.504 \quad (\text{Round to three decimal places as needed.})
\]

(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.)
Transcribed Image Text:To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 22 \) 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 \( \overline{x} = 36.6 \) and \( s = 10.6 \), compute the test statistic. \[ t_0 = -1.504 \quad (\text{Round to three decimal places as needed.}) \] (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.)
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