Question

In: Statistics and Probability

Construct the 92% confidence interval for mean of following data by assuming that the data follow...

Construct the 92% confidence interval for mean of following data by assuming that the data follow normal distribution. You have to use 92% Z value.

132, 135, 149, 133, 119, 121, 128, 132, 119, 110, 118, 137, 140, 139, 107, 116, 122, 124, 115, 103

Solutions

Expert Solution

The sample size is n = 20

The provided sample data along with the data required to compute the sample mean Xˉ and sample variance s^2 are

X

X2

132

17424

135

18225

149

22201

133

17689

119

14161

121

14641

128

16384

132

17424

119

14161

110

12100

118

13924

137

18769

140

19600

139

19321

107

11449

116

13456

122

14884

124

15376

115

13225

103

10609

Sum =

2499

315023

The sample mean Xˉ is computed as follows:

Also, the sample variance s^2 is

Therefore, the sample standard deviation s is

The provided sample mean is Xˉ=124.95

and the sample standard deviation is s = 12.08

The size of the sample is n = 20

and the required confidence level is 92%.

The number of degrees of freedom are df = 20 - 1 = 19

and the significance level is α=0.08.

Based on the provided information, the critical t-value is

                t_c = 1.85

The 92% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 92 % confidence for the population mean μ is

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