Question: Please follow the lab guidelines given on page 3. For full marks, your report for each hypothesis test problem must have the format given on

Please follow the lab guidelines given on page 3.

For full marks, your report for each hypothesis test problem must have the format given on the previous page.

1. Consider the variable HEIGHT in the 100students data set.

SEX AGE HEIGHT COINS KEYS CREDIT PULSE EXERCISE SMOKE COLOUR HAND 2 19 64 0 3 0 97 2 2 2 2 2 28 67.5 100 5 0 88 1 2 2 2 1 19 68 0 0 1 69 1 2 1 2 1 20 70.5 23 4 2 67 1 2 2 3 2 18 65 35 5 5 83 1 2 2 2 2 17 63 185 6 0 77 1 2 2 2 1 18 75 0 3 0 66 2 2 2 2 2 48 64 0 3 0 60 2 2 2 3 2 19 68.75 43 3 0 78 2 2 2 3 2 17 57 35 3 0 73 1 1 2 1 2 35 63 250 10 2 8 1 2 2 2 2 18 64 178 5 10 67 1 1 2 2 1 19 72 10 2 1 55 1 2 2 2 2 28 67 90 5 0 72 1 1 2 2 2 24 62.5 0 8 14 82 1 1 2 1 2 30 63 200 1 10 70 1 2 2 2 1 21 69 0 5 0 47 1 2 2 1 1 19 68 40 4 2 63 1 1 2 2 1 19 68 73 2 0 52 2 1 2 2 1 24 68 20 2 1 55 1 2 2 2 2 22 5 500 4 1 67 1 2 2 2 1 21 69 0 2 1 75 2 2 2 1 1 19 69 0 3 3 76 1 2 2 2 2 19 60 35 10 0 60 2 2 2 2 1 20 69 130 3 0 84 1 2 2 2 1 30 73 62 10 1 40 1 2 2 2 1 33 74 5 7 8 64 1 2 2 2 1 19 67 0 3 0 72 2 2 2 2 1 18 70 0 5 1 72 1 2 2 2 1 20 70 0 3 5 75 1 2 1 2 2 18 76 0 3 0 80 2 2 2 2 1 20 68 32 2 4 63 1 2 2 2 1 50 72 74 8 4 72 2 2 2 2 2 20 65 14 4 4 90 1 1 2 2 1 18 68 25 2 0 70 2 2 2 2 2 18 64 0 2 0 100 2 2 2 2 2 18 64 25 1 0 69 1 2 2 2 1 22 68 0 5 5 64 1 2 2 2 2 21 64 27 2 2 80 2 2 2 2 1 41 72 76 2 0 60 2 1 2 2 1 18 68 160 3 0 66 2 1 2 2 1 21 68 34 26 0 78 1 2 2 2 2 17 60 75 3 0 60 2 1 2 2 2 40 64 20 10 5 68 1 2 2 2 1 19 74 0 1 3 72 1 2 2 2 1 19 69 0 5 0 60 1 2 2 2 2 28 68 453 5 7 88 1 1 2 2 2 28 64 0 3 0 58 1 2 2 2 2 19 63 79 6 0 88 1 2 2 1 2 41 63 100 6 3 80 2 2 2 2 1 18 71 25 2 1 61 1 2 2 2 1 18 73 181 6 0 67 2 2 2 2 1 21 71 72 3 4 60 1 1 2 2 1 18 73 0 5 0 80 1 2 2 2 1 22 69 75 12 5 60 1 1 2 2 2 22 69 0 3 5 80 1 2 2 2 1 21 72 0 4 0 68 1 1 2 2 2 26 60 25 15 0 78 1 2 2 2 1 21 72 97 2 0 54 1 2 2 2 1 20 54 0 5 5 81 2 2 2 2 2 19 65 0 8 0 67 2 2 2 2 1 22 66 30 8 4 70 1 2 2 2 1 20 76 0 6 1 63 1 2 2 2 1 19 71 0 7 0 90 1 2 1 2 1 36 73 18 11 4 70 2 2 2 2 1 20 71 0 5 1 69 2 2 1 2 1 19 71 50 7 0 69 2 1 2 2 2 18 67.5 0 4 0 75 2 1 2 2 2 19 64 0 3 1 80 1 1 2 2 1 52 71.7 51 4 5 92 2 2 2 2 2 41 68 800 7 4 72 2 2 2 2 1 20 69 0 3 3 63 1 1 2 2 1 20 72 85 3 1 60 1 2 2 2 2 30 63 111 5 0 78 2 2 2 2 1 21 73 77 5 0 77 1 2 2 2 1 21 70 35 5 4 71 1 1 2 2 2 34 65.5 300 4 2 15 2 2 2 2 1 19 69 36 5 0 83 2 1 2 2 1 20 69 0 2 0 80 1 2 2 2 1 20 69 0 1 1 71 1 2 2 2 2 20 66 45 4 0 86 2 2 2 2 2 36 64.5 116 3 8 65 1 2 2 2 1 19 68 52 4 2 70 1 2 2 2 2 20 67 358 7 7 76 1 2 2 2 1 19 71 0 4 0 78 1 1 2 2 1 19 72 15 10 1 63 1 2 2 3 1 19 71 1 0 0 52 1 1 2 2 1 25 71 25 4 1 78 2 2 2 1 2 29 64 26 6 3 92 2 2 2 2 1 19 81 0 4 3 48 1 2 2 2 2 17 67.5 0 3 0 68 1 2 2 2 2 19 68 0 8 1 85 2 2 2 2 1 24 73 0 14 0 64 1 2 2 1 2 19 63 0 3 4 65 2 2 2 2 2 18 64 25 3 0 1 2 2 2 2 23 69 0 3 26 2 1 2 1 1 19 60 50 4 0 1 2 2 2 1 19 72 83 6 2 1 1 2 2 2 21 67 50 3 8 1 2 2 2 1 20 74 0 6 0 2 1 2 1

a) Make a normal qq-plot for HEIGHT and comment on whether the distribution is normal. Delete any outliers present so that the remaining values are normally distributed. Include all the probability plots you have made for HEIGHT. How many outliers did you remove?

b) Assume the population standard deviation is unknown. Use the cleaned up data set to compute a 95% confidence interval for the mean height of the population and then use this confidence interval to test the claim that the mean height is 69 at the significance level of 5%.

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