Question #18121
A random sample of 84 light bulbs had a mean life of 423 hrs with a standard deviation of 27hrs. Construct a 90% confidence interval for the mean life of all light bulbs of this type.
Expert's answer
we suppose that sample is ruled by student's distribution
so, step 1 is to check value of student's coefficient for alpha=1-0.9=0.1 and
degree of freedom = 423-1 = 422.
In tables you will find that it is approximately = 1.65
Next you have to divide your standard deviation by the square root of your
sample size.
that is 27/sqrt(423) = 1.31
now multiply them
1.33*1.65 = 4.851
So your 90% confidence interval is
84+-4.851/2 = 84+- 2.4
so, step 1 is to check value of student's coefficient for alpha=1-0.9=0.1 and
degree of freedom = 423-1 = 422.
In tables you will find that it is approximately = 1.65
Next you have to divide your standard deviation by the square root of your
sample size.
that is 27/sqrt(423) = 1.31
now multiply them
1.33*1.65 = 4.851
So your 90% confidence interval is
84+-4.851/2 = 84+- 2.4
Learn more about our help with Assignments: Statistics and Probability
