A producer of various kinds of batteries has been producing \"D\" size batteries
ID: 3326233 • Letter: A
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 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. 10. At 99% confidence using the critical value approach, test management's belief. What is the p-value associated with the sample results? What is your conclusion based on the p-value? a. b.Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 87
Alternative hypothesis: > 87
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 1.5
DF = n - 1
D.F = 35
t = (x - ) / SE
t = 1
tcritical = 2.72
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 1.0.
Interpret results. Since the t-value (0.19) is less than the critical value (2.72), we cannot reject the null hypothesis.
b)
Thus the P-value in this analysis is 0.162
Interpret results. Since the P-value (0.162) is greater than the significance level (0.01), we cannot reject the null hypothesis.
We can conclude that we do not have sufficient evidence in the favor of the claim that there is increase in life expectancy of batteries due to improved production process.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.