Question

The diameter of holes for a cable harness is known to have a normal distribution with o = 0.03 inches. A random sample of size 8 yields an average diameter of 1.5045 inches. Find a 99% two-sided confidence interval on the mean hole diameter. Round the answers to 4 decimal places. sus

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 1.5045

Population standard deviation =   $\sigma$ = 0.003

Sample size = n =8

At 99% confidence level the z is ,

$\alpha$  = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

Z_$\alpha$/2 = Z_0.005 = 2.576

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 2.576* ( 0.003/ $\sqrt$ 8)

= 0.0027

At 99% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

1.5045 -0.0027 < $\mu$ < 1.5045 +0.0027

1.5018< $\mu$ < 1.5072