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) is the probability of failing to reject the null hypothesis when it is false. Given that μ = 24, we calculate the z-score for the sample mean under the null hypothesis and find the probability of observing a sample mean less than the critical value. With a large sample size (n=36), the standard error is reduced, making it unlikely to fail to reject the null hypothesis when μ is actually 24. Hence, β is approximately 0.00.

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

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