MGMT2263

Worksheet #3

 

1)      A builder conducted a study in a major city in which the city was divided into different regions. One of the regions had a higher percentage of senior citizens than other regions of the city. He was concerned that the age standard deviation in this region might be less than in the others. The sample size of this region is 16 and the age standard deviation is 5.3 years. In another region chosen at random, the sample size is 13 and the age standard deviation is 7.2 years. Based on this evidence, is the age standard deviation in the first region significantly less than that of the second region? Test at a 5% level of significance.

(F = 1.8455; conclude the standard deviation for the region with the high percentage of seniors is not significantly less than that of the other region)

2)     Sales from two stores were gathered. Analysis of the data indicated both samples were normal. The summary statistics from the stores are:

 

Sample size

Mean

Std. Dev.

Store 1

9

45

4.1

Store 2

10

48

9.2

Is there any significant difference in the standard deviations of the stores’ sales? Test at a 5% level of significance. (F = 5.0351; conclude the standard deviations are not equal)

3)     A manufacturer is conducting a test of the tensile strengths of two types of copper coils. The summary statistics are:

 

Sample size

Mean

Std. Dev.

Coil A

9

118

17

Coil B

16

143

24

The tensile strengths are approximately normally distributed. Is there any significant difference in the average strengths of the two types? Test at a 5% level of significance. (t = 2.7496; conclude the average strengths of the two types are not equal)

4)     Is there a level of significance between 1% and 10% in which the opposite verdict would have been reached? (if the level of significance were set at 1%, the critical value would be 2.807 and the opposite conclusion would have been reached)

5)     Construct a 95% confidence interval of the mean difference in tensile strengths of the two types of coil. What conclusion would you reach based on the results of the confidence interval? (6.1881 < mB - mA < 43.8119; we would reject Ho since the hypothesized difference of 0 does not fall in the confidence interval)

6)     Let us return to the data from question 2 and test if there is any significant difference in the average sales of the 2 stores. Do not assume a level of significance. (t = -0.9333; p-value > 10%; conclude no significant difference in average sales of the 2 stores)

7)     A business magazine compared bonuses for 10 executives for the years 2006 and 2007. These were the results (in thousands of dollars):

CEO

2006 Bonus

2007 Bonus

#1

195

196

#2

183

160

#3

208

220

#4

190

195

#5

220

200

#6

235

250

#7

175

180

#8

150

145

#9

245

240

#10

210

230

Analysis of the data indicated they are normally distributed. Is there any significant difference in the average bonuses of the two years? Test at 5%.

(t = -0.1119; conclude there is no significant difference between the two years)

8)     Construct a 95% confidence of the difference between the two years. Round the limits to the nearest hundred. Interpret the interval. Why would the same conclusion be reached? (-10,600 < m2006 - m2007 < 9,600; we would not reject Ho since the hypothesized difference of 0 falls in the confidence interval)

9)     Suppose a level of significance had not been chosen. Why would the same conclusion be reached? (p-value > 10%; this provides strong support for Ho)

10)  A law firm wants to know if there is a difference in the number of typing mistakes made by two secretaries in the firm. Each secretary was given 5 randomly selected documents to type. The results were:

Secretary A

3

5

4

2

0

Secretary B

2

0

4

3

1

No assumptions about the normality of the data were made. Test at a 5%. level of significance. (p-value = 0.5476; no significant difference)

11)  Two samples of light bulbs are taken from two different brands. The following table gives the life of bulbs from the samples:

Brand A

1134

1255

1313

1012

1265

1375

1102

 

1107

1095

1401

1109

1150

 

 

Brand B

1405

1251

1106

1384

1193

1208

1110

 

1290

1210

1198

1203

1295

1102

1185

No assumptions about the normality of the data were made. Is there any significant difference in how long the bulbs from the 2 brands last? Test at a 5% level of significance. (Z = -0.8487; no significant difference)

12)  A psychologist conducts a seminar to increase a person’s self-esteem. A before-and-after test that measures a person’s self-esteem was given to nine randomly selected individuals. The results were:

 

#1

#2

#3

#4

#5

#6

#7

#8

#9

Before

70

72

75

61

82

55

43

51

84

After

74

88

71

62

89

58

41

63

80

No assumptions about the normality of the data were made. Is the seminar’s method effective? Test at a 5% level of significance. (T- = 12; conclude method not effective)

13)  A company tried a new reporting system to see if it would reduce the amount of time per day its salespeople spent doing paperwork. Here were the results in minutes:

 

#1

#2

#3

#4

#5

#6

#7

#8

#9

#10

Before

34

35

43

46

16

26

68

38

61

52

After

31

31

44

44

15

28

63

39

63

54

 

#11

#12

#13

#14

#15

#16

#17

#18

#19

#20

Before

42

19

20

26

40

51

24

29

48

19

After

38

21

19

22

38

50

21

33

51

18

No assumptions about the normality of the data were made. Is the system effective? Test at a 5% level of significance. (Z = 1.064; conclude system is not effective)