Question

In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 53 hours.

Find a 90% upper confidence interval for the mean lifetime. (Round the final answer to two decimal places.)

The 90% upper confidence bound is ____

I got 1226.75, but it says it incorrect.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1217

Population standard deviation =    = 53
Sample size = n =80

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

=0.1

Z = Z0.1 = 1.28( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.28 * (53 /  80 )

= 7.58
At 90% confidence interval estimate of the population mean
is,

+ E

1217 + 7.58

1224.58

upper bound=1224.58