Question

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1500 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 1490 hours with a population standard deviation of 80 hours. Test the manufacturers claim. Use a=0.05. Show graph as well.

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the mean lifetime of its fluorescent bulbs is 1500 hours.

Alternative hypothesis: Ha: the mean lifetime of its fluorescent bulbs is not 1500 hours.

H0: µ = 1500 versus Ha: µ ≠ 1500

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 1500

Xbar = 1490

σ = 80

n = 40

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (1490 – 1500)/[80/sqrt(40)]

Z = -0.7906

P-value = 0.4292

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the mean lifetime of its fluorescent bulbs is 1500 hours.