Find the 80% confidence interval

Question

 You intend to estimate a population mean 

 from the following sample.

91.7

77.6

90.6

85

71.5

86.8

81.6

80

76.1

84.7

77.2

84.1

79.2

84.8

74.7

80.1

63.8

89

74.6

78.9

79.7

74.7

78.1

79

87

86.9

83

96.4

78.6

95

72.1

82.3

86.5

76.8

82.1

89.4

86.8

83.4

76.5

87.9

86.6

62.9

91.7

86.1

82.2

83.5

85.9

Find the 80% confidence interval. Enter your answer as a tri-linear inequality accurate to two decimal place (because the sample data are reported accurate to one decimal place).

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Compute the mean and standard deviation of your sample

For sample size < 30 or population standard deviation unknown, you will use the t-distribution to determine the critical value for sample size - 1 degrees of freedom at tail alpha = 0.10.

For sample size > 30 and known population standard deviation, you will use the z-distribution to determine the critical value for probability = 0.90.

CI = mean +/- critical value * standard deviation/square root(sample size)