Question

In a random sample of 13 car owners, the mean monthly repair cost was $50.43 and the standard deviation was $17.54. Assume the population is normally distributed and use the t-distribution to find the margin of error at the 98% confidence level rounded to two decimal places. E =

Answer #1

Solution :

Given that,

= 50.43

s =17.54

n = Degrees of freedom = df = n - 1 =13 - 1 = 12

At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,12 = 2.681 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.681 * (17.54 / 13)

Margin of error = E= 13.04

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