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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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