Question

In: Statistics and Probability

A random sample of 80 car owners were asked how many years they had owned their...

A random sample of 80 car owners were asked how many years they had owned their current car. The results were ¯x=7x¯=7 years and s=2s=2. Estimate how long ago people typically acquired their car (at the 90% confidence level).

Here, we should use:

2-SampTInt
ZInterval
1-PropZInt
2-SampZInt
2-PropZInt
TInterval

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 7

sample standard deviation = s = 2

sample size = n = 80

Degrees of freedom = df = n - 1 = 80 - 1 = 79

Using T interval

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,79 = 1.664

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

= 1.664 * ( 2 / $\sqrt$ 80)

Margin of error = E = 0.37

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

± E

= 7 ± 0.37

= ( 6.63, 7.37)

orchestra answered 2 years ago

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