1) 2) For a sample of nine automobiles, the mileage (in 100s of miles) at which
ID: 3360808 • Letter: 1
Question
1)
2)
For a sample of nine automobiles, the mileage (in 100s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were born to 10% of their original thickness, the results are given in the following table: Automobile 1 Front Rear 32.8 26.6 35.6 36.4 29.2 40.9 40.9 34.836.6 41.2 35.2 46.1 46.0 39.9 51.7 51.6 46.1 47.3 a). Find a 95% confidence interval for the difference in mean lifetime between the front and the rear brake pads. (10 points) b). Write a conclusion about the obtained confidence interval. (5 pointsExplanation / Answer
Q2.
TRADITIONAL METHOD
given that,
sample mean, x =18.4
standard deviation, s =2.9136
sample size, n =10
I.
stanadard error = sd/ sqrt(n)
where,
sd = standard deviation
n = sample size
standard error = ( 2.9136/ sqrt ( 10) )
= 0.921
II.
margin of error = t /2 * (stanadard error)
where,
ta/2 = t-table value
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 9 d.f is 2.262
margin of error = 2.262 * 0.921
= 2.084
III.
CI = x ± margin of error
confidence interval = [ 18.4 ± 2.084 ]
= [ 16.316 , 20.484 ]
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DIRECT METHOD
given that,
sample mean, x =18.4
standard deviation, s =2.9136
sample size, n =10
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 9 d.f is 2.262
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 18.4 ± t a/2 ( 2.9136/ Sqrt ( 10) ]
= [ 18.4-(2.262 * 0.921) , 18.4+(2.262 * 0.921) ]
= [ 16.316 , 20.484 ]
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interpretations:
1) we are 95% sure that the interval [ 16.316 , 20.484 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean
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