A random sample of 81 cars traveling on a section of an interstate showed an average...

A random sample of 81 cars traveling on a section of an interstate showed an average speed of 68 mph. The distribution of speeds of all cars on this section of highway is normally distributed with a standard deviation of 10.5 mph.

The 94.52 confidence interval for μ is from _____ to ____?

Solutions

Expert Solution

Solution :

Given that,

= 68

s = 10.5

n =81

Degrees of freedom = df = n - 1 = 81 - 1 = 80

At 94.52% confidence level the t is ,

= 1 -94.52% = 1 - 0.9452 = 0.0548

/ 2 = 0.0548 / 2 = 0.0274

t /2,df = t0.0274,80 = 1.949

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

= 1.949 * (10.5 / $\sqrt$ 81)

= 2.3

Margin of error = 2.3

The 94.52% confidence interval estimate of the population mean is,

- E < < + E

68 - 2.3< < 68+ 2.3

65.7 < < 70.3

(65.7, 70.3 )

orchestra answered 1 year ago

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