Solved by verified expert :TEST QUESTIONS
31. A
sport preference poll yielded the following data for men and women. Use the 5%
significance level and test to determine is sport preference and gender are
independent.
Sport Preference
Basketball
Football
Soccer
Men
20
25
30
75
Gender
Women
18
12
15
45
38
37
45
120
32. Suppose
that we observe a random sample of size n from a normally distributed
population. If we are able to reject in favor of at the 5% significance
level, is it true that we can definitely reject in favor of the
appropriate one-tailed alternative at the 2.5% significance level? Why or why not?
33. An
investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock
is to measure the variation in the stock’s daily price changes. The investor obtains a random sample of 20
daily price changes for stock 1 and 20 daily price changes for stock 2. These data are shown in the table below. Show how this investor can compare the risks
associated with the two stocks by testing the null hypothesis that the
variances of the stocks are equal. Use = 0.10 and interpret the results of the statistical
test.
Day
Price Change
for stock 1
Price Change for
stock 2
1
1.86
0.87
2
1.80
1.33
3
1.03
-0.27
4
0.16
-0.20
5
-0.73
0.25
6
0.90
0.00
7
0.09
0.09
8
0.19
-0.71
9
-0.42
-0.33
10
0.56
0.12
11
1.24
0.43
12
-1.16
-0.23
13
0.37
0.70
14
-0.52
-0.24
15
-0.09
-0.59
16
1.07
0.24
17
-0.88
0.66
18
0.44
-0.54
19
-0.21
0.55
20
0.84
0.08
.
QUESTIONS 34 THROUGH 37 ARE BASED ON THE FOLLOWING INFORMATION:
BatCo (The Battery
Company) produces your typical consumer battery. The company claims that their batteries last
at least 100 hours, on average. Your
experience with the BatCo battery has been somewhat different, so you decide to
conduct a test to see if the companies claim is true. You believe that the mean life is actually
less than the 100 hours BatCo claims.
You decide to collect data on the average battery life (in hours) of a
random sample and the information related to the hypothesis test is presented
below.
Test of 100 versus one-tailed alternative
Hypothesized
mean
100.0
Sample
mean
98.5
Std
error of mean
0.777
Degrees
of freedom
19
t-test
statistic
-1.932
p-value
0.034
34. Can
the sample size be determined from the information above? Yes or no?
If yes, what is the sample size in this case?
35. You
believe that the mean life is actually less than 100 hours, should you conduct
a one-tailed or a two-tailed hypothesis test?
Explain your answer.
36. What
is the sample mean of this data? If you
use a 5% significance level, would you conclude that the mean life of the
batteries is typically more than 100 hours?
Explain your answer.
37. If
you were to use a 1% significance level in this case, would you conclude that
the mean life of the batteries is typically more than 100 hours? Explain your answer.
QUESTIONS 38 AND 39 ARE BASED ON
THE FOLLOWING INFORMATION:
Two teams of
workers assemble automobile engines at a manufacturing plant in Michigan. A random sample
of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar
random sample of 125 assemblies from team 2 shows 8 unacceptable
assemblies.
38. Construct
a 90% confidence interval for the difference between the proportions of
unacceptable assemblies generated by the two teams.
39. Based
on the confidence interval constructed in Question 38, is there sufficient
evidence o conclude, at the 10% significance level, that the two teams differ
with respect to their proportions of unacceptable assemblies?
.
40. Staples,
a chain of large office supply stores, sells a line of desktop and laptop
computers. Company executives
want to know whether the demands for these two types of computers are related
in any way. Each day’s demand for each type of computers is categorized as Low,
Medium-Low, Medium-High, or High. The data shown in the table below is based on
200 days of operation. Based on these data, can Staples conclude that demands
for these two types of computers are independent? Test at the 5% level of
significance.
Desktops
Low
Med-Low
Med-High
High
Low
3
14
14
4
35
Laptops
Med-Low
6
18
17
22
63
Med-High
13
16
11
16
56
High
8
14
15
9
46
30
62
57
51
200
