Answer:
(32.2,34.7)
Explanation:
Solution :
Given that,
\bar x = 33.4 hg
s = 6.4 hg
n = 177
Degrees of freedom = df = n - 1 = 177 - 1 = 176
At 99% confidence level the t is ,
α = 1 - 99% = 1 - 0.99 = 0.01
α / 2 = 0.01 / 2 = 0.005
tα /2,df = t0.005,176 = 2.604
Margin of error = E = tα/2,df * (s /√n)
= 2.604* ( 6.4/ √177)
= 1.25
The 95% confidence interval estimate of the population mean is,
\bar x - E < \mu < \bar x + E = 33.4 - 1.25 < \mu < 33.4 + 1.25
32.15 < \mu < 34.65
32.2 < \mu < 34.7
(32.2,34.7)