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.
Solution :
Given that,
Point estimate = sample mean =
= 65750
Population standard deviation =
= 4500
Sample size = n = 25
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2
* (
/n)
= 1.96* ( 4500 / 25
)
= 1764
At 95% confidence interval estimate of the population mean
is,
- E <
<
+ E
65750 - 1764 <
< 65750 + 1764
63986<
<67514
(63986 , 675 14)
6. You measure the lifetime (in miles of driving use) of a random sample of 25...
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