One important task in experiment design is to determine the sample size needed to support the conclusion. A manufacturer for a specific assistive device claims that its battery can last longer than 15 days without re-charging. To check if this claim is valid, a hypothesis test is conducted: H0: u≤15, Ha: u>15, and the significance level for the test is set to be 0.05. Let assume that the standard deviation sigma=1.6.
(a) Explain what Type I error and Type II error that may occur in this study.
(b) What is the probability of committing a type II error if its battery actual last for 14 days.
(c) What sample size you will need if it is intended for a 90% probability of detecting that ‘the u is less than 15’ when it was actually u=14.
Here are a few suggestions:
Type I errors result when you reject the null and it's true. Type II errors result when you accept the null and it's false. The probability of a Type II error is beta.
You may be able to find sample size using margin of error.
Formula is this:
Margin of error = (z-value)(sd/√n)