A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation $\sigma$= 6 months.To test the alternative hypothesis that μ

Question

A laptop battery lifespan follows a normal distribution with mean μ = 22 months and a standard deviation $\sigma$= 6 months.To test the alternative hypothesis that μ < 22 with α = .01, 36 laptop batteries are randomly selected.Assuming that μ = 24, the probability of type II error is approximately ________.
A)-.01
B)2.33
C)-4.33
D)0.01
E)0.00

Quizplus · Accepted Answer

The probability of a Type II error (β) in hypothesis testing is the probability of failing to reject the null hypothesis when it is false. Given the alternative hypothesis μ < 22 and assuming μ = 24 (which means the null hypothesis is false), the probability of a Type II error would be the probability of observing a sample mean close enough to 22 to fail to reject the null hypothesis, despite the true mean being 24. However, the specific calculation for this scenario involves finding the area under the normal distribution curve for the test statistic corresponding to the assumed true mean (μ = 24), given the sample size, standard deviation, and significance level. The provided choices do not include a numerical value that represents a valid probability for a Type II error, and the question seems to be incorrectly formatted or missing necessary information for a precise calculation. The correct answer choice provided here (E) suggests a probability of 0.00, which is not a realistic value for a Type II error in this context, indicating a possible error in the question or answer choices.

A Laptop Battery Lifespan Follows a Normal Distribution with Mean σ\sigmaσ

A Laptop Battery Lifespan Follows a Normal Distribution with Mean $\sigma$