Homework Sourse8 You receive a brochure from a large university The brochur
8-
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=0.010.01,
can you support the university\'s claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
3737
3131
2626
3131
3232
3939
2727
2525
2828
3030
3131
3333
3636
2828
3030
3030
2727
2222
(a) Write the claim mathematically and identify
Upper H 0H0
and
Upper H Subscript aHa.
Which of the following correctly states
Upper H 0H0
and
Upper H Subscript aHa?
A.
Upper H 0H0:
mugreater than or equals3232
Upper H Subscript aHa:
muless than<3232
B.
Upper H 0H0:
muequals=3232
Upper H Subscript aHa:
muless than<3232
C.
Upper H 0H0:
muequals=3232
Upper H Subscript aHa:
munot equals3232
D.
Upper H 0H0:
muless than or equals3232
Upper H Subscript aHa:
mugreater than>3232
E.
Upper H 0H0:
muless than<3232
Upper H Subscript aHa:
mugreater than or equals3232
F.
Upper H 0H0:
mugreater than>3232
Upper H Subscript aHa:
muless than or equals3232
(b) Use technology to find the P-value.
9-
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=0.010.01,
can you support the university\'s claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
3737
3131
2626
3131
3232
3939
2727
2525
2828
3030
3131
3333
3636
2828
3030
3030
2727
2222
(a) Write the claim mathematically and identify
Upper H 0H0
and
Upper H Subscript aHa.
Which of the following correctly states
Upper H 0H0
and
Upper H Subscript aHa?
A.
Upper H 0H0:
mugreater than or equals3232
Upper H Subscript aHa:
muless than<3232
B.
Upper H 0H0:
muequals=3232
Upper H Subscript aHa:
muless than<3232
C.
Upper H 0H0:
muequals=3232
Upper H Subscript aHa:
munot equals3232
D.
Upper H 0H0:
muless than or equals3232
Upper H Subscript aHa:
mugreater than>3232
E.
Upper H 0H0:
muless than<3232
Upper H Subscript aHa:
mugreater than or equals3232
F.
Upper H 0H0:
mugreater than>3232
Upper H Subscript aHa:
muless than or equals3232
(b) Use technology to find the P-value.
| 3737 | 3131 | 2626 | 3131 | 3232 | 3939 | 2727 | 2525 | 2828 | ||
| 3030 | 3131 | 3333 | 3636 | 2828 | 3030 | 3030 | 2727 | 2222 |
Solution
8.
a)
Formulating the null and alternative hypotheses,
Ho: u >= 32
Ha: u < 32 [ANSWER, A]
*************************
b)
As we can see, this is a left tailed test.
df = n - 1 = 17
Getting the test statistic, as
X = sample mean = 30.16666667
uo = hypothesized mean = 32
n = sample size = 18
s = standard deviation = 4.287464629
Thus, t = (X - uo) * sqrt(n) / s = -1.814166475
Thus, the p value is, as this is left tailed,
p = 0.043670535 [ANSWER, P VALUE]
