Question

The McCollough Corporation, 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, the management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.

a. Use a 0.01 level of significance to test for the evidence of improvement in the life expectancy of the batteries. Use the critical value criterion in your decision making.

[Hint: You need to (1) write the null and alternative hypotheses (2) know the significance level of the test (3) write the appropriate formula for the teststatistic (4) using the sample data, compute the numerical value of the teststatistic (5) look up the critical value, and finally (6) draw your conclusion].

b. What is the p-value of the test? Draw your conclusion using the p-value criterion.

Answer 1

1. Here claim is that mean is greater than 87

As null hypothesis always have equality sign, so hypothesis here is vs

2. Here it is given that use a 0.01 level of significance to test, so the significance level of the test is 0.01

3. As population standard deviation is known, the test statistics is z

4.

5. The z-critical value for a right-tailed test, for a significance level of α=0.01 is

zc​=2.33

Graphically

6. As test statistics do not fall in the rejection region, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is greater than 87

b.

As P value is greater than alpha we fail to reject the null hypothesis.

Hence we do not have sufficient evidence to support the claim that mean is greater than 87