Question

You receive a brochure from a large university. The brochure indicates that the mean class size for​ full-time faculty is fewer than 33 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 alphaequals0.10​, can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed. 38 29 27 35 35 37 26 22 29 25 32 36 34 30 29 33 26 26

​(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a. Which of the following correctly states Upper H 0 and Upper H Subscript a​? A. Upper H 0​: muequals33 Upper H Subscript a​: munot equals33 B. Upper H 0​: mugreater than33 Upper H Subscript a​: muless than or equals33 C. Upper H 0​: mugreater than or equals33 Upper H Subscript a​: muless than33 D. Upper H 0​: muequals33 Upper H Subscript a​: muless than33 E. Upper H 0​: muless than33 Upper H Subscript a​: mugreater than or equals33 F. Upper H 0​: muless than or equals33 Upper H Subscript a​: mugreater than33

​(b) Use technology to find the​ P-value. Pequals nothing ​(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? A. Fail to reject Upper H 0 because the​ P-value is greater than the significance level. B. Reject Upper H 0 because the​ P-value is less than the significance level. C. Fail to reject Upper H 0 because the​ P-value is less than the significance level. D. 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 33 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 33 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 33 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 33 students. Click to select your answer(s).

Answer 1

SolutionA:

fewer then 33 given its a left tail test

H0:

Ha:

alpha=0.10

mark option D

D. Upper H 0​: muequals33 Upper H Subscript a​: muless than33

SolutionB:

Use r software conduct t test for mean

Code is

number_of_people <- c(47,66,55,53,49,65,48,44,50,61,60,55)

t.test(classsize,mu=33,alternative = "less",conf.level = 0.90)

output:

One Sample t-test

data: classsize
t = -2.2659, df = 17, p-value = 0.0184
alternative hypothesis: true mean is less than 33
90 percent confidence interval:
-Inf 31.97115
sample estimates:
mean of x
30.5

p value=0.018

ANSWER:p value=0.018

Solutionc:

P=0.018

ALPHA=0.10

P<alpha

Reject Null hypthesis

mark option B

B. Reject Upper H 0 because the​ P-value is less than the significance level

Solutiond:

there is sufficient statistical evidence at 10% level of significance to support the claim.

MARK OPTION B

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 33 students.