Question

You receive a brochure from a large university. The brochure indicates that the mean class size for​ full-time faculty is fewer than 32students. 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=0.10​,can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

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=0.10​,

can you support the​ university's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

37	30	28	31	30	39	27	28	28
29	29	35	30	32	25	31

A. Write the claim mathematically and identify H0 and Ha.

B. Use technology to find the​ P-value.

Answer 1

A. claim : the mean class size for​ full-time faculty is fewer than 32

H0:$\mu$ = 32

Ha:$\mu$ <32 (one tailed )

B ) using excel>addin>phstat>one sample test

we have

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	32
Level of Significance	0.1
Sample Size	16
Sample Mean	30.5625
Sample Standard Deviation	3.687252817
Intermediate Calculations
Standard Error of the Mean	0.9218
Degrees of Freedom	15
t Test Statistic	-1.5594
Lower-Tail Test
Lower Critical Value	-1.3406
p-Value	0.0699
Reject the null hypothesis

the value of test stat t = -1.5594

p value = 0.0699

SInce p value is less than 0.10 so we reject Ho . and accept the claim.