The lifetime of a squirrel follows a normal distribution with mean μ months and a standard deviation $\sigma$=7 months.To test the alternative hypothesis that μ 40, 25 squirrels are randomly selected.The null hypothesis is rejected when the sample mean is bigger than 43.Assuming that μ=45, the probability of type II error is approximately _________.
A)0.076
B)0.016
C)0.05
D)0.011
E)0.983

Question

The lifetime of a squirrel follows a normal distribution with mean μ months and a standard deviation $\sigma$=7 months.To test the alternative hypothesis that μ > 40, 25 squirrels are randomly selected.The null hypothesis is rejected when the sample mean is bigger than 43.Assuming that μ=45, the probability of type II error is approximately _________.
A)0.076
B)0.016
C)0.05
D)0.011
E)0.983

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 = 45, we calculate the z-score for the sample mean of 43 using the formula: z = (X̄ - μ) / (σ/√n). Substituting the values, z = (43 - 45) / (7/√25) = -2.857. Using the standard normal distribution table, the probability corresponding to z = -2.857 is approximately 0.076.

The Lifetime of a Squirrel Follows a Normal Distribution with Mean