# T-Test for Mean Lifetime of its Lithium Batteries is 1400 Hours

There will be at least one question of this type on my final exam tomorrow and I need a logical way to approach the solution.

Question: A Manufacturer claims that the mean lifetime of its Lithium batteries is 1400 hours. A homeowner select s 25 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 80 hours. Test the manufacturers claim. Use alpha = 0.05.

Round the test statistic to the nearest thousandth.

A) State your hypothesis: I believe it s Ho: mean = 1400 and H1: mean <1400

B) Calculate your test statistic.

C) Use either the p-value or classical approach to determine whether to reject or not.

(Explain and show all you steps)

I would like to see how to use both methods but especially the classical approach

D) Use appropriate language to state your conclusion.

Thank you,

Allan Cook

https://brainmass.com/statistics/type-i-and-type-ii-errors/t-test-for-mean-lifetime-lithium-batteries-596503

#### Solution Preview

Hypothesis testing

There will be at least one question of this type on my final exam tomorrow and I need a logical way to approach the solution.

Question: A Manufacturer claims that the mean lifetime of its Lithium batteries is 1400 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1380 hours with a standard deviation of 80 hours. Test the manufacturers claim. Use alpha = 0.05. Round the test statistic to the nearest thousandth.

A) State your hypothesis: I ...

#### Solution Summary

This solution includes a detailed explanation for one sample t test. Concepts covered in this posting involve: null and alternative hypotheses, level of significance, P-value, t test statistics, decisions about rejecting or not rejecting the null hypothesis.