Respuesta :
Answer:
Sample size of at least 49 must be needed .
Step-by-step explanation:
We are given that a 98% confidence interval is constructed with a margin of error equal to 3,000 miles. Assume the standard deviation for the tire life of this particular brand is 9,000 miles.
So, Margin of error formula is given by = [tex]Z_\frac{\alpha}{2}* \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\alpha[/tex] = significance level which is 2%
[tex]\sigma[/tex] = standard deviation = 9,000 miles
n = sample size
Here, the value of z score at 2% significance level is 2.3263 .
So, margin of error = 2.3263 * [tex]\frac{9000}{\sqrt{n} }[/tex]
[tex]\sqrt{n}[/tex] = [tex]\frac{2.3263*9000}{ 3000}[/tex]
= 6.9789
n = [tex]6.9789^{2}[/tex] = 48.7 or ≈ 49 (approx)
Therefore, sample size of at least 49 must be needed .
