Question

6. You measure the lifetime (in miles of driving use) of a random sample of 25...

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.

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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 = Z0.025 = 1.96   ( Using z table )


Margin of error = E = Z\alpha/2 * ( \sigma /\sqrtn)

= 1.96* ( 4500 /  \sqrt25 )

= 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)

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