ECON 216202
Statistics (II)
Spring 2024
Assignment 01
Due Date: Tuesday, March 26, 2024
1. Two independent simple random samples are taken to test the difference between the
means of two populations whose variances are not known, but are assumed to be equal. The
sample sizes are n1 = 31 and n2 = 40. The correct distribution to use is the t distribution with
_____ degrees of freedom.
a. 73
b. 72
c. 71
d. 69
2. Salary information regarding male and female employees of a large company is shown
below.
Male
Female
Sample Size
64
36
Sample Mean Salary (in $1000)
45
41
Population Variance ( )
128
72
The standard error of the difference between the two sample means is
a. 4.
b. 7.46.
c. 4.24.
d. 2.0.
3. The following information was obtained from matched samples taken from two
populations.
The daily production rates for a sample of workers before and after a training program are
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shown below. Assume the population of differences is normally distributed.
Worker
Before
After
1
20
22
2
25
23
3
27
27
4
23
20
5
22
25
6
20
19
7
17
18
The point estimate for the difference between the means of the two populations is
a. -1.
b. -2.
c. 0.
d. 1.
4. A statistics teacher wants to see if there is any difference in the abilities of students
enrolled in statistics today and those enrolled five years ago. A sample of final examination
scores from students enrolled today and from students enrolled five years ago was taken. You
are given the following information.
Today
Five Years Ago
82
88
2
σ
112.5
54
n
45
36
The test statistic for the difference between the two population means is
a. -.47.
b. -.65.
c. -1.5.
d. -3.0.
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5. The following information was obtained from independent random samples taken of two
populations.
Assume normally distributed populations with equal variances.
Sample 1
Sample 2
Sample Mean
45
42
Sample Variance
85
90
Sample Size
10
12
The 95% confidence interval for the difference between the two population means is (use
rounded standard error)
a. -5.344 to 11.344.
b. -5 to 3.
c. -4.86 to 10.86.
d. -2.65 to 8.65.
6. The management of a department store is interested in estimating the difference between
the mean credit purchases of customers using the store's credit card versus those customers
using a national major credit card. You are given the following information.
Store's Card
Major Credit Card
Sample size
64
49
Sample mean
$140
$120
Population standard deviation
$10
$8
A 95% confidence interval estimate for the difference between the average purchases of all
customers using the two different credit cards is
a. 13.31 to 16.69.
b. 11.68 to 18.32.
c. 12.22 to 17.78.
d. 16.68 to 23.32.
7. In order to determine whether or not there is a significant difference between the mean
hourly wages paid by two companies (of the same industry), the following data have been
accumulated.
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Company A
Company B
Sample size
80
65
Sample mean
$16.75
$16.25
Population standard deviation
$1.00
$.95
The p-value is
a. .0010.
b. .0021.
c. .0042.
d. .9990.
8. The results of a recent poll on the preference of shoppers regarding two products are shown
below.
Shoppers Favoring
Product
Shoppers Surveyed
A
800
560
B
900
612
The standard error of
-
This Product
is
a. .025.
b. .044.
c. .0225.
d. .68.
9. The results of a recent poll on the preference of teenagers regarding the types of music they
listen to are shown below.
Teenagers Favoring
Music Type
Teenagers Surveyed
Pop
800
384
Rap
900
450
This Type
The point estimate of the difference between the two population proportions is
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a. -.02.
b. .048.
c. .52.
d. -.5.
10. Generally, the ________ sample procedure for inferences about two population means
provides better precision than the _______ sample approach.
a. single, independent
b. independent, pooled
c. matched, independent
d. matched, pooled
11. We are interested in testing whether the variance of a population is significantly less than
1.44. The null hypothesis for this test is
a. H0: σ2 < 1.44.
b. H0: s2 ≥ 1.44.
c. H0: σ < 1.20.
d. H0: σ2 ≥ 1.44.
12. The random variable for a chi-square distribution may assume
a. any value between -1 to 1.
b. any value between -∞ to +∞.
c. any negative value.
d. any value greater than zero.
13. The manager of the service department of a local car dealership has noted that the service
times of a sample of 30 new automobiles has a standard deviation of 5 minutes. A 95%
confidence interval estimate for the standard deviation of the service times (in minutes) for all
their new automobiles is
a. 16.047 to 45.722.
b. 15.857 to 45.180.
c. 3.982 to 6.722.
d. 22.833 to 65.059.
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14. The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of
significance and a sample size of 25 is
a. 33.196.
b. 36.415.
c. 39.364.
d. 37.652.
15. The 99% confidence interval estimate for a population variance when a sample standard
deviation of 12 is obtained from a sample of 10 items is
a. 4.589 to 62.253.
b. 46.538 to 422.171.
c. 54.941 to 746.974.
d. 62.042 to 562.895.
16. A sample of 61 observations yielded a sample standard deviation of 6. If we want to test
H0: σ2 = 40, the test statistic is
a. 54.
b. 9.15.
c. 54.90.
d. 9.
17. Based on the sample evidence below, we want to test the hypothesis that population A has
a larger variance than population B.
Sample A
Sample B
N
11
10
2
12.1
5
s
The p-value is approximately
a. .10.
b. .05.
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c. .025.
d. .01.
18. To avoid the problem of not having access to tables of the F distribution when a onetailed test is required and with F values given for the lower tail, let the
a. smaller sample variance be the numerator of the test statistic.
b. larger sample variance be the numerator of the test statistic.
c. sample variance from the population with the smaller hypothesized variance be
the numerator of the test statistic.
d. sample variance from the population with the larger hypothesized variance be the
numerator of the test statistic.
19. Consider the following hypothesis problem.
n = 30
H0: σ2 = 500
s2 = 625
Ha: σ2 ≠ 500
At the 5% level of significance, the null hypothesis
a. should be rejected.
b. should not be rejected.
c. should be revised.
d. should not be tested.
20. Consider the following sample information from Population A and Population B.
Sample A
Sample B
n
24
16
s2
32
38
We want to test the hypothesis that the population variances are equal. At the 10% level of
significance, the null hypothesis
a. should be rejected.
b. should not be rejected.
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c. should be revised.
d. should not be tested.
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