Answer to Question #127464 in Statistics and Probability for ASHISH

Question

In a random selection of 64 of the 2400 intersections in a small city, the mean number of scooter accidents per year was 3.2 and the sample standard deviation was 0.8

a. Make an estimate of the standard deviation of the population from the sample standard deviation.

b. Work out the standard error of mean for this finite population.

c. If the desired confidence level is 0.90, what will be the upper and lower limit of the confidence interval for the mean number of accidents per intersection per year?

Answer 1

a.

The best point estimate of the standard deviation of the population is the standard deviation of the sample itself.

So $\sigma=0.8$

b.

Standard error of mean is

$\sigma_{X} = \frac{\sigma}{\sqrt{n}}\times\sqrt{\frac{N-n}{N-1}} = \frac{0.8}{\sqrt{64}}\times\sqrt{\frac{2400-64}{2400-1}} \approx 0.097$

c.

For 90% confidence interval $z=1.645$

Lower bound is $\overline{X}-z\times\sigma_X = 3.2-1.645\times0.097 \approx 3.04$

Upper bound is $\overline{X}-z\times\sigma_X = 3.2+1.645\times0.097 \approx 3.36$