Question

Construct the indicated confidence interval for the population mean

muμ

using the​ t-distribution. Assume the population is normally distributed.

c=0.99

x overbarxequals=14.4

s=0.88

nequals=12

Answer 1

The provided sample mean is and the sample standard deviation is s=0.88. The size of the sample is n=12 and the required confidence level is 99%.

The number of degrees of freedom are df=12−1=11, and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df=11 degrees of freedom is tc​=3.106

The 99% confidence for the population mean \muμ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean \muμ is

CI=(14.4 - 0.789, 14.4 + 0.789)

CI=(13.611, 15.189)

Hence, 13.611< <15.189

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