Question

no calculators please! need to know how to work it out the long way, thank you!

A simple random sample of 50 items from a population with σ-6 resulted in a sample mean of 32. a. Provide a 90% confidence interval for the population mean. b. Provide a 95% confidence interval for the population mean c. Provide a 99% confidence interval for the population mean. 2,

Answer 1

Solution:-

xbar = 32, σ = 6, n = 50

a) 90% confidence interval for the population mean is C.I = (30.604, 33.396).

$C.I = \bar{x}\pm z_{\alpha /2}\times \frac{S.D}{\sqrt{n}}$

C.I = 32 + 1.645 × 0.848528

C.I = 32 + 1.3958

C.I = (30.604, 33.396)

b) 95% confidence interval for the population mean is C.I = (30.337, 33.663).

$C.I = \bar{x}\pm z_{\alpha /2}\times \frac{S.D}{\sqrt{n}}$

C.I = 32 + 1.96 × 0.848528

C.I = 32 + 1.6631

C.I = (30.337, 33.663)

c) 99% confidence interval for the population mean is C.I = (29.815, 34.185).

$C.I = \bar{x}\pm z_{\alpha /2}\times \frac{S.D}{\sqrt{n}}$

C.I = 32 + 2.575 × 0.848528

C.I = 32 + 2.18496

C.I = (29.815, 34.185)