MGMT2263

Worksheet #4

 

1)     An auto manufacturer with 2 plants wanted to compare the percentage of scrap widgets between them. They collected samples at the plants. These were the results:

 

Sample size

Number of scrap widgets

Plant #1

500

6

Plant #2

500

8

Is there any significant difference in the percentage of scrap widgets at the 2 plants? Test at 5%. (Z = -0.5383; conclude no significant difference)

2)     Construct a 95% confidence interval of the difference of proportions between plant #2 and plant #1. Interpret what it means. (-1.1% < p2 – p1 < 1.9% ; We are 95% confident that the percentage of scrap widgets for plant #2 ranges from 1.1% less to 1.9% more than plant #1)

3)     Suppose they want to see if the difference in the percentage of scrap chips between Plant #2 and Plant #1 was significantly more than 1%. Use a p-value approach. (p-value = 0.791; conclude the spread is not more than 1%)

4)     A real estate company wanted to compare average sales among its three locations. For a randomly selected month, the number of sales for each salesperson from each location was recorded. The results were:

Office A

2

5

6

3

 

 

Office B

1

4

3

3

2

2

Office C

2

2

2

3

1

 

If it can be assumed that the data is normally distributed and that the three offices share the same standard deviation, is there any significant difference in the average sales of the three offices? Test at 5%. (F = 3.2343; conclude no significant difference in the average sales of the three offices)

 

5)     A school board wanted to compare average grades between four schools in different regions of its jurisdiction. Eight grades were randomly selected from each school The results were:

School A

49

72

59

65

80

70

86

78

School B

58

92

76

60

80

50

52

54

School C

66

98

97

76

88

69

86

62

School D

96

82

89

92

74

76

93

94

a)      Analysis of the data indicates that each school’s grades are normally distributed and they share a common standard deviation. Is there any significant difference in the average grades of the four schools? Test at 5%. (F = 4.7792; conclude there is a significant difference between the average grade of the four schools)

b)     Between which schools is there a significant difference? Why is this consistent with the results of ANOVA? (B and D)

c)      What is the common standard deviation among the four schools? (12.753)

d)     Construct a 95% confidence interval of the difference between school D and school B. Does the confidence interval seem to be consistent with the results of the hypothesis test? (8.6883 < mD - mB < 34.8117; seems consistent since mD - mB = 0 does not fall in the confidence interval)

6)     In a survey, salespeople for a company were asked to estimate the average amount of time each week they do various tasks. Here were the results for 6 of the salespeople:

 

Paperwork

Handling returns

Meeting with clients

Person #1

32

34

52

Person #2

22

32

48

Person #3

27

27

46

Person #4

19

37

52

Person #5

13

34

53

Person #6

24

42

50

Analysis of the data showed it to be normally distributed.

a)      Is there any significant difference in the average amount of time spent on each task? Test at a 5%. level of significance (F = 42.1; conclude there is a significant difference in time spent on the tasks)

b)     Based on Tukey’s test, which pairs of tasks are significantly different? (All 3 tasks are significantly different)

c)      Is there any significant difference in the average amount of time spent by the salespeople on these tasks? Test at 5%.(F = 0.81; conclude no significant difference between the salespeople)

7)     A restaurant owner wants to determine which of gender and annual income contributes to how much people spend per week on average eating out. A survey had the following results:

 

Male

Female

< $25K

28.20

22.33

 

31.47

37.66

 

37.19

40.40

 

16.90

28.59

$25K to under $50K

40.11

31.75

 

45.12

28.09

 

29.14

30.42

 

27.80

30.06

$50K or more

39.92

33.52

 

43.69

41.36

 

52.10

46.17

 

46.02

38.63

a)      Does the average amount spent depend on gender? Test at a 5% level of significance. (F =0.7627; conclude the amount spent does not depend on gender)

b)     Does the average amount spent depend on income? Test at a 5% level of significance. (F = 7.5822; conclude the amount spent depends on income)

c)      Is there significant interaction between income and gender? Test at a 5% level of significance. (F = 1.2811; conclude there is no significant interaction between income and gender)