Question

The Buffalo, New York, Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling.

14	24	24	19	24	7	31	20	26	23	23	28	16	15	21

Develop a 98% confidence interval for the population mean

Confidence interval is between _________ and _______

Answer 1

Mean = X / n

= 315 / 15

= 21

Standard deviation S = Sqrt [ X² - n ² / n-1 ]

= Sqrt [ (7135 - 15 * 21² / 14 ]

= 6.0945

Degrees of freedom df = n-1 = 15 - 1 = 14

t critical value at 0.02 significance level with 14 df = 2.624

98% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

21 - 2.624 * 6.0945 / sqrt(15) < < 21 + 2.624 * 6.0945 / sqrt(15)

16.87 < < 25.13

98% CI is ( 16.87 , 25.13)

95% CI is between 16.87 and 25.13