You and a childhood friend invent a new type of cell phone battery, and your tea

Question

You and a childhood friend invent a new type of cell phone battery, and your team believes the new battery can last longer than 30 hours in continuous use. You want to test this claim before you start marketing the battery, so you decide to produce n=100 batteries and evaluate the mean battery life. Accordingly, your null hypothesis is H0: mu<=30 and the alternative hypothesis is H1:mu>30. However, your friend wants to save money on this trial and use a small number of batteries for the test (n<100), but your production manager believes you should use a larer number of batteries (n>100). What are the pros and cons of these two positions? Who do you think is right?

Explanation / Answer

While performing the hypothesis testing, standard error is one of the important metric that decides the rejection region. and it is calculated as sigma/sqrt(n)

the threshold value of rejection xbar = mean + z * SE

as we see more the value of n, xbar will be nearer to the mean. If we increase the valeu of n very high, this may result into Type II error i.e. rejecting the null hypothesis incorrectly. And if the value of n is considerably small, this results into type I error i.e. accepting the null hypothesis incorrectly.

Best approach is to balance the test with least type II error because it is more dangerous for hypothesis test.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.