Question

The driving distances (in miles) to work of 30 people are shown in the table at the left. Assume the population standard deviation is 8 miles. Find (a) the point estimate of the population mean m and (b) the margin of error for a 95% confidence interval. only use four rows of data

Driving distances to work (in miles) 12 9 7 2 8 7 3 27 21 10 13 7 2 30 7 6 13 6 4 1 10 3 13 6 2 9 2 12 16 18

Answer 1

Answer

(A) Point estimate of mean of population is equal to $\mu_x$

$\mu_x$ = (sum of all data values in first four rows)/(total number of data values in first four rows)

this implies

$\mu_x$ =(12+9+7+2+8+7+3+27+21+10+13+7+2+30+7+6+13+6+4+1+10+3+13+6)/24

= 227/24

= 9.46 (rounded to 2 decimal places)

(B) Population standard deviation $\sigma = 8$

Margin of error ME = $z *(\sigma / \sqrt{n})$

where z = 1.96 for 95% confidence interval (using z distribution table)

n = 24 (sample size for first four rows)

and $\sigma = 8$ (population standard deviation)

this implies

ME = $1.96*(8/\sqrt{24})$

$=1.96*1.633$

$=3.20$ (rounded to 2 decimals)