Question

You receive a brochure from a large university. The brochure indicates that the mean class size for​ full-time faculty is fewer than 32 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 alpha equals 0.10​, can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed. 34 31 29 33 35 40 23 25 31 28 33 35 35 31 30 33 30 22 ​(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a. Use technology to find the​ P-value. Decide whether to reject or fail to reject the null hypothesis. Which of the following is​ correct? A. Reject Upper H 0 because the​ P-value is less than the significance level. B. Fail to reject Upper H 0 because the​ P-value is less than the significance level. C. Reject Upper H 0 because the​ P-value is greater than the significance level. D. Fail to reject Upper H 0 because the​ P-value is greater than the significance level. ​(d) Interpret the decision in 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 32 students. B. At the 10​% level of​ significance, there is sufficient evidence to support the claim that the mean class size for​ full-time faculty is fewer than 32 students. C. At the 10​% level of​ significance, there is sufficient evidence to support the claim that the mean class size for​ full-time faculty is more than 32 students. D. 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 32 students.

Answer 1

From the given sample data : Sample size=n=32

Sample mean=

Sample standard deviation=s=

Also ,

Hypothesized value=

Significance level=

a) Hypothesis : VS

b) The test statistic is ,

c) P-value = ; From excel "=TDIST(0.9404,17,1)"

Rejection Rule : If P-value < , then reject Ho , accept otherwise

Decision : Fail to reject Ho because P-value greater than the significance level.

(d) Interpretation :

D. 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 32 students.