Question

4) We want a 99% confidence interval for the average amount of time (in minutes) spent commuting to work in a large city. The interval is to have a margin of error of no more than 3 minutes, and the amount of time spent commuting has a normal distribution with a standard deviation  = 18 minutes. What numbers of observations are required?

Answer 1

Answer: 239

Step-by-step explanation:

Given : Confidence level : 99%

Significance level : $\alpha=1-0.99=0.01$

Margin of error : E = 3 minutes

Population standard deviation : $\sigma=18$

To find : Numbers of observations are required. (Minimum Sample size)

Formula : $n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2$

Using z-value table,

Two-tailed z-value for $\alpah=0.01$ : $z_{\alpha/2}=2.576$

Using given values , we get

$n=(\dfrac{2.576\cdot18}{3})^2\\\\=(15.456)^2\\\\=238.887936\spprox239$

Hence, the minimum number of observation is required = 239