A researcher wishes to test H₀: $\mu$
= 50 versus H_a: $\mu$
> 50.A sample will be taken from a normally distributed population with mean $\mu$
= 53 and standard deviation is $\sigma$
= 15.If the researcher wishes both the probability of a Type I error and the probability of a Type II error to be 0.05,what sample size should they take?

Question

A researcher wishes to test H₀:

\mu

= 50 versus H_a:

\mu

> 50.A sample will be taken from a normally distributed population with mean

\mu

= 53 and standard deviation is

\sigma

= 15.If the researcher wishes both the probability of a Type I error and the probability of a Type II error to be 0.05,what sample size should they take?

Quizplus · Accepted Answer

Given the requirements for both Type I and Type II errors to be 0.05, and the population parameters, the calculation involves finding the sample size that satisfies these conditions. The Z-scores for Type I error (alpha) and Type II error (beta) can be used along with the standard deviation and the difference in means to calculate the required sample size. The correct calculation leads to a sample size that ensures both errors are at the desired levels, which is 271 in this case.

A Researcher Wishes to Test H0 μ\muμ = 50 Versus Ha μ\muμ

A Researcher Wishes to Test H₀ $\mu$ = 50 Versus H_a $\mu$