Respuesta :
Because the population standard deviation is not known, the student's t distribution is used for the critical value.
We want the margin of error to be 2 mpg at 90% confidence level (2-tailed).
An estimate of the sample standard deviation is s = 3, therefore the margin of error is calculated as
[tex]t^{*} \frac{s}{\sqrt{n}} =2[/tex]
where t* is obtained from a table for the t distribution.
n = sample size.
With s=3, obtain
n = 2.25 (t*)².
Note that the degree of freedom is df = n-1.
Because df depends on t*, the value of n should be determined iteratively.
Calculations for n are shown in the following table.
Trial df t* n
------ ----- -------- --------
1 100 1.66 6.2
2 5 2.015 9.136
3 8 1.86 7.784
4 7 1.895 8.08
After 4 iterations, df=7 and n=8
Answer: 8 cars should be tested.
We want the margin of error to be 2 mpg at 90% confidence level (2-tailed).
An estimate of the sample standard deviation is s = 3, therefore the margin of error is calculated as
[tex]t^{*} \frac{s}{\sqrt{n}} =2[/tex]
where t* is obtained from a table for the t distribution.
n = sample size.
With s=3, obtain
n = 2.25 (t*)².
Note that the degree of freedom is df = n-1.
Because df depends on t*, the value of n should be determined iteratively.
Calculations for n are shown in the following table.
Trial df t* n
------ ----- -------- --------
1 100 1.66 6.2
2 5 2.015 9.136
3 8 1.86 7.784
4 7 1.895 8.08
After 4 iterations, df=7 and n=8
Answer: 8 cars should be tested.
