You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At a = 0.10, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 34 26 27 35 33 37 28 23 270 25 31 34 30 32 27 30 28 28 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H,? O B. Ho: H= 31 Ha: u31 O A. Ho: u=31 Ос. Но: и> 31 Ha:us31 HaiH<31 O E. Ho: H<31 Hg:H2 31 OF. Ho: us31 Hạ: u> 31 O D. Ho: H231 Hạ: H<31 (b) Use technology to find the P-value. P=D (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? O A. Reject Ho because the P-value is greater than the significance level. O B. Fail to reject Ho because the P-value is less than the significance level. OC. Reject Ho because the P-value is less than the significance level. O D. Fail to reject Ho because the P-value is greater than the significance level. (d) Interpret the decision in the context of the original claim. O A. At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students. O B. At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31 students. OC. At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size for D. At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size for
You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At a = 0.10, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 34 26 27 35 33 37 28 23 270 25 31 34 30 32 27 30 28 28 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H,? O B. Ho: H= 31 Ha: u31 O A. Ho: u=31 Ос. Но: и> 31 Ha:us31 HaiH<31 O E. Ho: H<31 Hg:H2 31 OF. Ho: us31 Hạ: u> 31 O D. Ho: H231 Hạ: H<31 (b) Use technology to find the P-value. P=D (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? O A. Reject Ho because the P-value is greater than the significance level. O B. Fail to reject Ho because the P-value is less than the significance level. OC. Reject Ho because the P-value is less than the significance level. O D. Fail to reject Ho because the P-value is greater than the significance level. (d) Interpret the decision in the context of the original claim. O A. At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students. O B. At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31 students. OC. At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size for D. At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size for
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Statistical Testing of University Class Size Claims**
You receive a brochure from a large university claiming that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are as follows:
- Class Sizes: 34, 26, 27, 35, 33, 37, 28, 23, 27, 25, 31, 34, 30, 32, 27, 30, 28, 28
Assumption: The population is normally distributed.
### (a) Formulate the Hypotheses
Identify the null and alternative hypotheses (H₀ and Hₐ) mathematically:
- **C.** \( H₀: \mu > 31 \)
\( Hₐ: \mu \leq 31 \)
### (b) Calculation of the P-value
Use technology to find the P-value:
\[ \text{P-value} = \boxed{\text{(Round to three decimal places as needed.)}} \]
### (c) Decision on the Null Hypothesis
Decide whether to reject or fail to reject the null hypothesis based on the P-value and significance level (\( \alpha = 0.10 \)):
- **A.** Reject \( H₀ \) because the P-value is greater than the significance level.
- **B.** Fail to reject \( H₀ \) because the P-value is less than the significance level.
- **C.** Reject \( H₀ \) because the P-value is less than the significance level.
- **D.** Fail to reject \( H₀ \) because the P-value is greater than the significance level.
### (d) Interpretation
Interpret the decision within the context of the original claim:
- **A.** At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students.
- **B.** At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31 students.
- **C.** At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda6faddd-a84f-4d8b-94b7-6f2c3fcecfb0%2Fb3a41769-d134-4b62-953c-9e5405cb471d%2F8ovslyv_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Testing of University Class Size Claims**
You receive a brochure from a large university claiming that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are as follows:
- Class Sizes: 34, 26, 27, 35, 33, 37, 28, 23, 27, 25, 31, 34, 30, 32, 27, 30, 28, 28
Assumption: The population is normally distributed.
### (a) Formulate the Hypotheses
Identify the null and alternative hypotheses (H₀ and Hₐ) mathematically:
- **C.** \( H₀: \mu > 31 \)
\( Hₐ: \mu \leq 31 \)
### (b) Calculation of the P-value
Use technology to find the P-value:
\[ \text{P-value} = \boxed{\text{(Round to three decimal places as needed.)}} \]
### (c) Decision on the Null Hypothesis
Decide whether to reject or fail to reject the null hypothesis based on the P-value and significance level (\( \alpha = 0.10 \)):
- **A.** Reject \( H₀ \) because the P-value is greater than the significance level.
- **B.** Fail to reject \( H₀ \) because the P-value is less than the significance level.
- **C.** Reject \( H₀ \) because the P-value is less than the significance level.
- **D.** Fail to reject \( H₀ \) because the P-value is greater than the significance level.
### (d) Interpretation
Interpret the decision within the context of the original claim:
- **A.** At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is more than 31 students.
- **B.** At the 10% level of significance, there is not sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 31 students.
- **C.** At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size
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