Question

A sample of 15 speeds measured from the southbound traffic on I-65 near downtown Montgomery have a sample mean of 62.5 miles/hour. The population standard deviation is known to be 4.5 miles/hour. The speed limit on this area of the road is 55 miles/hour. Calculate a 90% confidence interval for the mean speed.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 62.5

Population standard deviation =    = 4.5

Sample size = n = 15

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 4.5 /  15 )

= 1.91

At 90% confidence interval estimate of the population mean is,

  ± E

62.5 ± 1.91

( 60.59, 64.41)