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MBALN 603 Statistics Examination

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Question

Part 1

Keywords:Confidence Intervals for Means, Normal distribution, t-student distribution

Exercise 1. (5 points) For the following data set

114

112

123

111

109

103

112

113

107

129

108

126

131

129

126

115

123

108

131

115

134

133

132

114

104

127

128

137

114

139

128

117

121

110

141

121

138

140

122

130

115

102

Table 1:  Data set Exercise 1

Construct a

  1. 90%confidence interval for the population mean;
  2. 95%confidence interval for the population mean;
  3. 99%confidence interval for the population mean;
  4. Whatassumption do you need to make about the population of interest to construct the confidence intervals ?

Exercise 2. (5 points) For the following data set

136

141

137

145

131

135

138

136

130

132

136

134

137

133

141

139

Table 2:  Data set Exercise 2

Construct a

1. 90%confidence interval for the population mean;

2. 95%confidence interval for the population mean;

3. 99%confidence interval for the population mean;
 
4.Whatassumption do you need to make about the population of interest to construct the confidence intervals

Exercise 3. (5 points) Two boxes, A and B contain equal numbers of balls (black and white). A sample of 100 balls selected with replacement from each of the boxes revealed 52 white balls form box A and 44 white balls from box B.

  1. Testthe hypothesis that the two boxes have equal ratio of white balls, using a significance level of 0.05
  2. Testthe hypothesis that box A has greater ratio of white balls than box B, using a significance level of 0.05

Exercise 4. (5 points) Consider the sample data for grades A, B, C & D of four different classes, which are tabulated in table 3. Test whether the four means are equal at the 0.05 level of significance.

Perform a test that will compare all 4 means at once. We are not interested in pair-wise comparisons at this stage.

Please show all the steps in your calculations.

Table 3:  Data set Exercise 4

80

81

83

78

83

79

72

79

80

83

80

80

65

76

81

98

92

65

87

57

81

74

68

81

65

34

68

71

34

45

78

91

57

61

51

46

71

69

66

72

71

59

63

82

81

67

61

52

72

75

64

 

81

80

74

 

36

55

78

 

83

67

 

 

91

94

 

 

73

 

 

 

51

 

 

 

98

 

 

 

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