MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Need help with part (b) please. Thanks

### Hypothesis Testing on a Sample Mean with a Single Population

To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample size of \( n = 21 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).

#### t-Distribution Area in Right Tail
(There is an instruction to click to view, but since this is text, you would presumably click on a link or button in the webpage for further details on the t-distribution area in the right tail.)

---

#### Part (a)

If \( \bar{x} = 105 \) and \( s = 9.8 \), compute the test statistic.

\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{105 - 100}{9.8 / \sqrt{21}} \approx 2.338 \]

(Round to three decimal places as needed)

#### Part (b)

If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, determine the critical values.

The critical values are:
\[ \pm 2.831 \]

(Use a comma to separate answers as needed. Round to three decimal places as needed.)

---

For more detailed steps, you might include how to obtain the t-value from a t-distribution table or any software output, and also how to determine the critical values using the degrees of freedom (df = n-1).
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Transcribed Image Text:### Hypothesis Testing on a Sample Mean with a Single Population To test \( H_0: \mu = 100 \) versus \( H_1: \mu \neq 100 \), a simple random sample size of \( n = 21 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). #### t-Distribution Area in Right Tail (There is an instruction to click to view, but since this is text, you would presumably click on a link or button in the webpage for further details on the t-distribution area in the right tail.) --- #### Part (a) If \( \bar{x} = 105 \) and \( s = 9.8 \), compute the test statistic. \[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{105 - 100}{9.8 / \sqrt{21}} \approx 2.338 \] (Round to three decimal places as needed) #### Part (b) If the researcher decides to test this hypothesis at the \( \alpha = 0.01 \) level of significance, determine the critical values. The critical values are: \[ \pm 2.831 \] (Use a comma to separate answers as needed. Round to three decimal places as needed.) --- For more detailed steps, you might include how to obtain the t-value from a t-distribution table or any software output, and also how to determine the critical values using the degrees of freedom (df = n-1).
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