MGMT2263 Tutorial Sheet #3

 

1)     A health center wanted to see if there was any difference in the average weight of its clients at two of its locations after taking its program. They randomly selected 10 people from each location and weighed them. The results were:

Person

1

2

3

4

5

6

7

8

9

10

Location A

194

126

153

170

136

174

132

164

138

155

Location B

128

129

157

181

185

194

105

129

172

137

Analysis of the data indicated the data was normally distributed. Is there any significant difference in the average weight of the clients between the two locations? (t = 0.2131; conclude no significant difference)

2)     An apartment hunter wanted to compare average rents for 1- and 2-bedroom apartments. She got rents from 8 of each type and got the following:

1 bed

641

612

657

688

686

702

584

643

2 bed

814

867

604

982

1001

854

853

611

Do 2-bedroom apartments cost significantly on average more than 1-bedroom apartments? Conduct all appropriate tests at the 5% level of significance. Assume the data is normally distributed. (t = 3.1604; conclude 2 bed cost more on average)

3)     Suppose a level of significance had not been chosen in the previous question. Why would the same conclusion be reached? (p-value < 1%)

4)     Construct a 95% confidence interval of the average difference in the costs of 2-bedroom and 1-bedroom apartments. Interpret the interval. (46.40 < m2 - m1 < 296.86; with 95% confidence, 2-bedroom apartments cost from $46.40 to $296.86 more per month on average than 1-bedroom apartments)

5)     A real estate firm tried a new filing system to see if its agents would spend less time on paperwork on average. For one particular week, these were the results (in minutes):

Agent

1

2

3

4

5

6

7

8

9

10

11

12

13

Before

113

94

99

77

81

91

111

104

85

66

111

51

109

After

109

100

86

80

95

106

117

107

85

84

125

66

108

Analysis of the data indicates that the times are normally distributed. Is the system effective? Test at a 5% level of significance. (t = -2.3117; do not reject Ho; conclude system not effective)

6)     Why would the p-value for the previous question be more than 50%?

7)     Construct a 95% confidence interval of the average difference between the period after the new system was introduced and before. Interpret the interval. (0.3 < m(after) - m(before) < 11.3; with 95% confidence, the agents spend as much as 11 minutes more per week on average on paperwork after the program was introduced than before)

8)     Ten people were asked to compare 2 movies on a scale from 1 to 10, 10 being best. Here are the results:

Person

1

2

3

4

5

6

7

8

9

10

Movie A

5

6

9

4

8

7

7

2

6

8

Movie B

4

4

8

3

7

7

6

3

5

8

Is there any significant difference in how the movies are ranked? Test at a 5% level of significance. (T=4; conclude movies not equally ranked)

9)     For a museum, respondents were first asked how likely they would be to visit it on a scale from 1 to 5 where 1 is not at all likely and 5 is very likely. Then we described exhibits to them and asked them the same question as before. Suppose the results for 20 respondents were:

Person

1

2

3

4

5

6

7

8

9

10

Before

1

2

5

1

1

1

1

1

3

2

After

3

1

2

3

4

3

3

4

2

2

Person

11

12

13

14

15

16

17

18

19

20

Before

2

2

1

1

1

2

1

2

1

2

After

3

2

3

3

2

5

2

4

4

2

Is there a significant improvement in the rating? Conduct at a 5% level of significance.  (Z = 2.6273; conclude there is a significant improvement)

10)  In a focus group, people from two economically different neighbourhoods were asked how often they eat out in a month. They sampled 6 people from each type of neighbourhood. The results were:

Person

1

2

3

4

5

6

Richer

15

10

12

16

13

8

Poorer

5

9

9

8

4

5

No assumptions about the normality of the data were made. Do the people in the richer neighbourhood eat out more often than those in the poorer neighbourhood? Do not specify a level of significance. (p-value = 0.0076; conclude richer neighbourhood eat out more)

11)  A psychologist wanted to see if hearing impaired children are more visually acute than children with normal hearing. The data measures eye movement rates with higher rates meaning the person is more visually acute. Twelve children were randomly selected from each type. The results are:

Person

1

2

3

4

5

6

7

8

9

10

11

12

Hearing impaired

3.25

2.75

2.75

3.14

3.23

2.30

2.64

1.95

2.17

2.45

1.83

2.23

Normal hearing

2.35

1.56

1.15

1.65

1.43

1.83

1.75

1.23

2.03

1.64

1.96

1.37

Are children who are hearing impaired more visually acute than children with normal hearing? Do not make any assumptions about the normality of the data. Test at a 5% level of significance. (Z = 3.6084; conclude hearing impaired more visually acute)