Question

A producer of various kinds of batteries has been producing "D" size
batteries with a life expectancy of 87 hours. Due to an improved
production process, management believes that there has been an
increasein the life expectancy of their "D" size batteries. A sample
of 36 batteries showed an average life of 88.5 hours. It is known that
the standard deviation of the population is 9 hours.

a.

Give the null and the alternative hypotheses.

b.

Compute the test statistic.

c.

At the 1% level of significance using the critical value approach,
test management's belief.

d.

What is the p-value associated with the sample results? What is your
conclusion based on the p-value using α = .01?
e.What is your conclusion based on the p-value using α = .05?

Answer 1

Here in this scenario note that the population standard deviation is known and the sample size is large enough 36 then here to test the claim of manegement we have to conduct the one sample z test as below,

Conclusion :

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ life expectancy of D size battery is greater than 87, at the 0.01 significance level.

Thank you.