Question

Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed.

c=0.95, x bar=12.2, s=0.53, n=19

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Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12.2

sample standard deviation = s = 0.53

sample size = n = 19

Degrees of freedom = df = n - 1 = 18

t _/2,df = 2.101

Margin of error = E = t_/2,df * (s /n)

= 2.101 * (0.53 / 19)

Margin of error = E = 0.26

The 95% confidence interval estimate of the population mean is,

- E < < + E

12.2 - 0.26 < < 12.2 + 0.26

11.94 < < 12.46

(11.94 , 12.46)