Question

An electrical firm manufactures a certain type of LED light bulb and claims that the average bulb lifetime is at least 800 hours. To test this, a random sample of 60 bulbs is taken. The average life of the sample is found to be 788 hours with a standard deviation of 40 hours.

(a)  At a level of 0.05 significance, is there compelling evidence to doubt the comp any's claim? Be sure to state the appropriate hypotheses, and specify the rejection region.

(b)  How many bulbs should be tested if it is desired that the power of the test be 99% when the actual average lifetime is 795 hours.

Answer 1

Let denotes the average bulb lifetime of LED lights.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

Rejection region :

We reject H₀ at 5% level of significance if

The value of the test statistic

and critical value

We can also write the rejection region is :

Since , we reject H₀ at 5% level of significance and we can conclude that the average bulb lifetime of LED lights is significantly less than 800 hours and there is compelling evidence to doubt the company's claim.

Power

Now,

(ans)