five measurements are taken of the octane rating for a parti

five measurements are taken of the octane rating for a particular type of gasoline. the results in (%) are 87.0, 86.0, 86.5, 88.0, 85.3.

a) find a 99% two-sided confidence interval for the mean octane rating for this type of gasoline.

b) find a 99% lower confidence interval for the mean octane rating for this type of gasoline.

c) what assumptions are you making to justify the inferences in parts (a) and (b)

(a) sample size=n=5

sample mean=86.56

sample standard deviation =1.021274

The degree of freedom =n-1=5-1=4

Given a=0.01, t(0.005, df=4) =4.60 (from student t table)

So 99% confidence interval is

xbar +/- t*s/vn

--> 86.56 +/- 4.60*1.021274/sqrt(5)

--> (84.45905, 88.66095)

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(b) Given a=0.01, t(0.01, df=4) =3.75 (from student t table)

So a 99% lower confidence interval is

xbar - t*s/vn

=86.56 - 3.75*1.021274/sqrt(5)

=84.84727

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