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 α=0.01​,can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.   38 30 31 33 29 41 29 27 29     26 27 36 36 27 25 29 25 22           ​(a) Write the claim mathematically and identify H0 andHa.   Which of the following correctly states H0 and Ha​?   A. H0​:μ=32 Ha​:μ≠32   B. H0​:μ<32 Ha​:μ≥32   C. H0​:μ>32 Ha​:μ≤32   D. H0​:μ≥32 Ha​:μ<32   E. H0​: μ≤32 Ha​: μ>32   F. H0​: μ=32 Ha​: μ<32   ​(b) Use technology to find the​ P-value. P=____ ​(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. 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. Fail to reject H0 because the​ P-value is greater than the significance level.   D. Reject H0 because the​ P-value is less than the significance level.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
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 α=0.01​,can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.
 
38
30
31
33
29
41
29
27
29
 
 
26
27
36
36
27
25
29
25
22
 
 
 
 
 
​(a) Write the claim mathematically and identify H0 andHa.
 
Which of the following correctly states H0 and Ha​?
 
A.
H0​:μ=32
Ha​:μ≠32
 
B.
H0​:μ<32
Ha​:μ≥32
 
C.
H0​:μ>32
Ha​:μ≤32
 
D.
H0​:μ≥32
Ha​:μ<32
 
E.
H0​: μ≤32
Ha​: μ>32
 
F.
H0​: μ=32
Ha​: μ<32
 
​(b) Use technology to find the​ P-value.
P=____
​(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. 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. Fail to reject H0 because the​ P-value is greater than the significance level.
 
D. Reject H0 because the​ P-value is less than the significance level.
Expert Solution
Step 1

Claim : The brochure indicates that the mean class size for​ full-time faculty is fewer than 32 students, i.e. μ<32

So the hypothesis is , 

H0 : μ = 32

Ha : μ < 32

Left tailed test. 

Since population standard deviation (σ ) is not known we have to run "One sample t test " 

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman