Question

A quality control engineer finds that a sample of 100 batteries had an average lifetime of 470 hours. Assuming a population standard deviation of σ = 25 hours, test whether the population mean is 480 hours vs. the alternative hypothesis µ < 480.

Answer 1

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

The null and alternative hypotheses are given as below:

H0: µ = 480 versus Ha: µ < 480

This is a lower tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 480

Xbar = 470

σ = 25

n = 100

α = 0.05

Critical value = -1.6449

(by using z-table or excel)

Z = (470 - 480)/[25/sqrt(100)]

Z = -4

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that batteries had an average lifetime less than 480 hours.