Question

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

Answer 1

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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