You receive a brochure from a large university. The brochure indicates that the

Question

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 3232 students. You want to test this claim. You randomly select 1818 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At alphaequals=0.050.05, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

36 25 28 33 33 40 25 27 32 31 31 34 36 29 26 30 28 22

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At alphaequals=0.050.05, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
12.6 9.4 12.5 7.5 4.8 10.7 12.3 8.6

A humane society claims that less than 37% of U.S. households own a dog. In a random sample of 409 U.S. households, 155 say they own a dog. At alphaequals=0.10, is there enough evidence to support the society's claim?
(a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscript aHa. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

One study, based on responses from 1,011 randomly selected teenagers, concluded that 39% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.

Explanation / Answer

Q.
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 1818 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At alphaequals=0.05, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
36 25 28 33 33 40 25 27 32 31 31 34 36 29 26 30 28 22

A.

Given that,
population mean(u)=32
sample mean, x =30.3333
standard deviation, s =4.589
number (n)=18
null, Ho: =32
alternate, H1: <32
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.74
since our test is left-tailed
reject Ho, if to < -1.74
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =30.3333-32/(4.589/sqrt(18))
to =-1.541
| to | =1.541
critical value
the value of |t | with n-1 = 17 d.f is 1.74
we got |to| =1.541 & | t | =1.74
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.5409 ) = 0.07087
hence value of p0.05 < 0.07087,here we do not reject Ho

ANSWERS
---------------
null, Ho: =32
alternate, H1: <32
test statistic: -1.541
critical value: -1.74
decision: do not reject Ho
p-value: 0.07087

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