ECO 380 Business Statistics
Gulf University for Science & Technology Department of Economics & Finance
Assignment 5 (LO iii)
 When developing an interval estimate for the difference between two sample means, with sample sizes of n_{1} and n_{2},
 n_{1} must be equal to n_{2}
 n_{1} must be smaller than n_{2}
 n_{1} must be larger than n_{2}
 n_{1} and n_{2} can be of different sizes,
ANS: D
 To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n_{1} be the size of sample 1 and n_{2} the size of sample 2)
 (n_{1} + n_{2}) degrees of freedom
 (n_{1} + n_{2}  1) degrees of freedom
 (n_{1} + n_{2}  2) degrees of freedom
 None of the above
ANS: C
Exhibit 101
Salary information regarding male and female employees of a large company is shown below.
Male 
Female 

Sample Size 
64 
36 
Sample Mean Salary (in $1,000) 
44 
41 
Population Variance () 
128 
72 
 Refer to Exhibit 101. The point estimate of the difference between the means of the two populations is
 28
 3
 4
 4
ANS: B
 Refer to Exhibit 101. The standard error for the difference between the two means is
 4
 46
 24
 0
ANS: D
 Refer to Exhibit 101. At 95% confidence, the margin of error is
 96
 645
 920
 000
ANS: C
 Refer to Exhibit 101. The 95% confidence interval for the difference between the means of the two populations is
 0 to 6.92
 2 to 2
 1.96 to 1.96
 0.92 to 6.92
ANS: D
 Refer to Exhibit 101. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is
 0
 5
 96
 645
ANS: B
 Refer to Exhibit 101. The pvalue is
 0668
 0334
 336
 96
ANS: A
 Refer to Exhibit 101. At 95% confidence, the conclusion is the
 average salary of males is significantly greater than females
 average salary of males is significantly lower than females
 salaries of males and females are not equal
 None of these alternatives is correct.
ANS: D
Exhibit 102
The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.
Worker Before After
Worker  Before  After 

1  20  22 
2  25  23 
3  27  27 
4  23  20 
5  22  25 
6  20  19 
7  17  18 
 Refer to Exhibit 102. The point estimate for the difference between the means of the two populations is
 1
 2
 0
 1
ANS: C
 Refer to Exhibit 102. The null hypothesis to be tested is H_{0}: _{}_{} = 0. The test statistic is
 1.96
 96
 0
 645
ANS: C
 Refer to Exhibit 102. Based on the results of question 11 and 5% significance level, the
 null hypothesis should be rejected
 null hypothesis should not be rejected
 alternative hypothesis should be accepted
 None of these alternatives is correct.
ANS: B
Exhibit 10 3
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} 112.5 54 n 45 36
 Refer to Exhibit 103. The point estimate for the difference between the means of the two populations is
 58.5
 9
 9
 6
ANS: D
 Refer to Exhibit 103. The standard error of is
 9
 3
 4
 2
ANS: D
 Refer to Exhibit 103. The 95% confidence interval for the difference between the two population means is
 a. 9.92 to 2.08
 3.92 to 3.92
 13.84 to 1.84
 24.228 to 12.23
ANS: A PTS: 1 TOP: Inference  Means
 Refer to Exhibit 103. The test statistic for the difference between the two population means is
 .47
 .65
 1.5
 3
ANS: D
 Refer to Exhibit 103. The pvalue for the difference between the two population means is
 .0013
 .0026
 .4987
 .9987
ANS: B
 Refer to Exhibit 103. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)
 There is a statistically significant difference in the average final examination scores between the two classes.
 There is no statistically significant difference in the average final examination scores between the two classes.
 It is impossible to make a decision on the basis of the information given.
 There is a difference, but it is not significant.
ANS: A Exhibit 104
The following information was obtained from independent random samples. Assume normally distributed populations with equal variances.
Sample 1 Sample 2
Sample Mean 45 42
Sample Variance 85 90
Sample Size 10 12
 Refer to Exhibit 104. The point estimate for the difference between the means of the two populations is
 0
 2
 3
 15
 Refer to Exhibit 104. The standard error of is
 0
 0
 372
 48
 Refer to Exhibit 104. The degrees of freedom for the tdistribution are
 23
 24
 20
 Refer to Exhibit 104. The 95% confidence interval for the difference between the two population means is
 5.372 to 11.372
 5 to 3
 4.86 to 10.86
 2.65 to 8.65
 Refer to Exhibit 106. A point estimate for the difference between the mean purchases of the users of the two credit cards is
 2
 18
 265
 15
 Refer to Exhibit 106. At 95% confidence, the margin of error is
 694
 32
 96
 15
 Refer to Exhibit 106. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is
 49 to 64
 68 to 18.32
 125 to 140
 8 to 10
 Refer to Exhibit 109. The mean for the differences is
 50
 5
 0
 5
 Refer to Exhibit 109. The test statistic is
 645
 96
 096
 616
 Refer to Exhibit 109. At 90% confidence the null hypothesis
 should not be rejected
 should be rejected
 should be revised
 None of these alternatives is correct.
ANS: C
ANS: B

22
ANS: D
ANS: A
Exhibit 106
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 
$125 
Population standard deviation 
$10 
$8 
ANS: D
ANS: B
ANS: B Exhibit 109
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.
Driver  Manufacturer A  Manufacturer B 

1  32  28 
2  27  22 
3  26  27 
4  26  24 
5  25  24 
6  29  25 
7  31  28 
8  25  27 
ANS: C
ANS: D
ANS: A
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