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ECO 380 Business Statistics

Gulf University for Science & Technology
Department of Economics & Finance

Assignment 5 (LO iii)

  1. When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,
  1. n1 must be equal to n2
  2. n1 must be smaller than n2
  3. n1 must be larger than n2
  4. n1 and n2 can be of different sizes,

ANS: D

  1. 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 n1 be the size of sample 1 and n2 the size of sample 2)
  1. (n1 + n2) degrees of freedom
  2. (n1 + n2 - 1) degrees of freedom
  3. (n1 + n2 - 2) degrees of freedom
  4. None of the above

ANS: C

Exhibit 10-1

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

  1. Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is
  1. -28
  2. 3
  3. 4
  4. -4

ANS: B

  1. Refer to Exhibit 10-1. The standard error for the difference between the two means is
  1. 4
  2. 46
  3. 24
  4. 0

ANS: D

  1. Refer to Exhibit 10-1. At 95% confidence, the margin of error is
  1. 96
  2. 645
  3. 920
  4. 000

ANS: C

  1. Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is
  1. 0 to 6.92
  2. -2 to 2
  3. -1.96 to 1.96
  4. -0.92 to 6.92

ANS: D

  1. Refer to Exhibit 10-1. 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
  1. 0
  2. 5
  3. 96
  4. 645

ANS: B

  1. Refer to Exhibit 10-1. The p-value is
  1. 0668
  2. 0334
  3. 336
  4. 96

ANS: A

  1. Refer to Exhibit 10-1. At 95% confidence, the conclusion is the
  1. average salary of males is significantly greater than females
  2. average salary of males is significantly lower than females
  3. salaries of males and females are not equal
  4. None of these alternatives is correct.

ANS: D  

Exhibit 10-2

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

WorkerBeforeAfter
12022
22523
32727
42320
52225
62019
71718
  1. Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is
  1. -1
  2. -2
  3. 0
  4. 1

ANS: C

  1. Refer to Exhibit 10-2. The null hypothesis to be tested is H0:  = 0. The test statistic is
  1. -1.96
  2. 96
  3. 0
  4. 645

ANS: C

  1. Refer to Exhibit 10-2. Based on the results of question 11 and 5% significance level, the
  1. null hypothesis should be rejected
  2. null hypothesis should not be rejected
  3. alternative hypothesis should be accepted
  4. 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

  1. Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations is
  1. 58.5
  2. 9
  3. -9
  4. -6

ANS: D

  1. Refer to Exhibit 10-3. The standard error of is
  1. 9
  2. 3
  3. 4
  4. 2

ANS: D

  1. Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is
  1. a. -9.92 to -2.08
  2. -3.92 to 3.92
  3. -13.84 to 1.84
  4. -24.228 to 12.23

ANS: A PTS: 1 TOP: Inference - Means

  1. Refer to Exhibit 10-3. The test statistic for the difference between the two population means is
  1. -.47
  2. -.65
  3. -1.5
  4. -3

ANS: D

  1. Refer to Exhibit 10-3. The p-value for the difference between the two population means is
  1. .0013
  2. .0026
  3. .4987
  4. .9987

ANS: B

  1. Refer to Exhibit 10-3. 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.)
  2. There is a statistically significant difference in the average final examination scores between the two classes.
  3. There is no statistically significant difference in the average final examination scores between the two classes.
  4. It is impossible to make a decision on the basis of the information given.
  5. There is a difference, but it is not significant.

ANS: A Exhibit 10-4

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

  1. Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is
    1. 0
    2. 2
    3. 3
    4. 15

    ANS: C

    1. Refer to Exhibit 10-4. The standard error of is
    1. 0
    2. 0
    3. 372
    4. 48

    ANS: B

    1. Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are
      22
    1. 23
    2. 24
    3. 20

    ANS: D

    1. Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means is
    1. -5.372 to 11.372
    2. -5 to 3
    3. -4.86 to 10.86
    4. -2.65 to 8.65

    ANS: A

    Exhibit 10-6

    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

    $125

    Population standard deviation

    $10

    $8

    1. Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards is
    1. 2
    2. 18
    3. 265
    4. 15

    ANS: D

    1. Refer to Exhibit 10-6. At 95% confidence, the margin of error is
    1. 694
    2. 32
    3. 96
    4. 15

    ANS: B

    1. Refer to Exhibit 10-6. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is
    1. 49 to 64
    2. 68 to 18.32
    3. 125 to 140
    4. 8 to 10

    ANS: B Exhibit 10-9

    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
    13228
    22722
    32627
    42624
    52524
    62925
    73128
    82527
    1. Refer to Exhibit 10-9. The mean for the differences is
    1. 50
    2. 5
    3. 0
    4. 5

    ANS: C

    1. Refer to Exhibit 10-9. The test statistic is
    1. 645
    2. 96
    3. 096
    4. 616

    ANS: D

    1. Refer to Exhibit 10-9. At 90% confidence the null hypothesis
    1. should not be rejected
    2. should be rejected
    3. should be revised
    4. None of these alternatives is correct.

    ANS: A

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