Question

"D" size batteries produced by MNM Corporation have had a life expectancy of 84.5 hours. An improved production process in intended to increase in the life expectancy of its "D" sized batteries, but before fill production begins, the firm would like to determine whether the process actually increases battery life. A Sample of 64 batteries showed an everage life of 87 hours. Assume from past information that it is known that the standard deviation of the population is 16 hours.

a) Formulate the hypothesis for this problem

b) Compute the test statistic

c) What is the p-value associated with the sample results?

d) What is your conclusion based on the p-value? Let a= 0.05.

On this problem the instructor has stated "For each question listed, explain how to get the correct answer. Think of this like an essay question. Or like you’re tutoring somebody. That’s what I’m really shooting for—for you to understand the material well enough to explain it to somebody else. If you can show me you can do that, you will get full credit.

So the answer has to be in essay form or comprehensive form. explaining the variables and how i got to the answer.

Answer 1

(a)

The life expentency of batteries is 84.5 hours.

The clam is that an improved proction process inceases the lifeexpectancy from 84.5 hours to a higher value.

The claim always is given in the Alternative Hypothesis.

Thus, we got the two hypothesis as follows:

H0: Null Hypothesis: 84.5

HA: Alternative Hypothesis: 84.5

(b)

Standard Error (SE) is the Standard Deviation of the distribution of sample means. It is obtained by dividing the Standard Deviation () of the population by the squareroot of the sample size (n) as given below:

SE = /

= 16/ = 2

Test statistic is the Normalized form of the difference between the sample mean () from thepopulation mean (). The normalisation is achieved by dividing the difference between sample mean () and population mean () by Standard Error (SE) as given below:

Test statistic is:
Z =(87 - 84.5)/2 = 1.25

(c)

For deriving the p-value from Zscore first we look at the Table of Area Under Stadard Normal Curve and get the area corresponding to the achieved Z score as follows:

Table of Area Under Standard Normal Curve gives area = 0.3944

Next step is: Since this is a One tail - Right SideTest, we subtract the area got from 0.5 to obtain the p - value as give below:

So,

p-value = 0.5 - 0.3944 = 0.1056

(d)

The rejection region is definedasbelow:
Reject null hypothesis if p-value is less than Significance level ().

Here:

Since p-value = 0.1056 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that an improved production process increases the life expectancy of its "D" sized batteries.