(a) Given
Sample size n = 100
Sample mean \(\overline{x}\) = 15
Population SD σ = 5
The 95% confidence interval for the population mean is \(\overline{x}\) \(\pm\) Zα/2 σ√n
Here Zα/2 = 1.96. So we get
= 15 ± (1.96) ( 5/√100)
= 15 ± (1.96) (0.5)
= 15 ± 0.98
= 14.02 and 15.98
Therefore 95% confidence interval for population mean µ is (14.02, 15.98)
The 99% confidence interval is \(\overline{x}\) \(\pm\) 2.58 σ√n
= 15 ± 2.58 (5/√100)
= 15 ± 2.58 (0.5)
= 13.71 and 16.29
Therefore 99% confidence interval for the population mean µ is (13.71, 16.29)
(b) If population S.D a is not known, then the sample S.D can be used in the place of o in estimating the confidence interval.