Question 9-15 are based on the random sample below which is obtained to test the following hypothesis about the population mean.

80 100 81 93 80 57 98 90

71 56 58 78 59 55 55 77

72 78 56 94 98 59 93 86

89 62 60 66 59 71 96 97

94 69 64 77 87 77 64 90

90 95 98 99 56 69 72 81

95 89 97 83 98 58 88 90

90 57 99 80 88 58 69 75

85 91 67 70 73 86 83 62

90 88 75 56 57 57 92 67

70 67 71 64 70 68 99 83

91 98 100 67 75 92 79 70

92 97 59 70 68 59 71 99

Test the hypothesis that the mean is less than 80.

1. The estimated variance of the mean is,

2. The value of the test statistic is (if negative use the absolute value):

3. Given = 0.05, the critical value for the test is,

4. The approximate p-value for the test is,

5. Based on the p-value in the previous question,