Question

6. You measure the lifetime (in miles of driving use) of a random sample of 25 tires of a certain brand. The sample mean is 65,750 miles. Suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown mean μ and standard deviation σ = 4,500 miles. Find a 95% confidence interval for the population mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 65750

Population standard deviation =   $\sigma$ = 4500

Sample size = n = 25

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96   ( Using z table )

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

= 1.96* ( 4500 /  $\sqrt$25 )

= 1764
At 95% confidence interval estimate of the population mean
is,

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

65750 - 1764 <  $\mu$ < 65750 + 1764

63986<  $\mu$ <67514

(63986 , 675 14)