Question

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

Answer 1

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 /n)

= 1.664 * ( 2 / 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)