Question

Suppose it is known from experience that the standard deviation of the weight of 10-ounce packages of cookies is 2.5 ounces. To check whether or not the true average is, on a given day, 10 ounces, employees selected a random sample from the packages. For the significance level α=0.05, when the average is 12.5 ounces, the power of the test is 0.90 . What is the sample size for this study?

Answer 1

To find the sample size for this study, use the formula for calculating power in hypothesis testing and the formula for a one-sample t-test.

Step-by-step explanation:

To find the sample size for this study, we need to use the formula for calculating power in hypothesis testing:

Power = 1 - β = 1 - P(Type II Error) = 0.90

To find the sample size, we can use a power calculation formula, such as the one for a one-sample t-test:

n = [((Zα + Zβ)σ/δ)^2] / [(μ0 - μa)^2]

Given that the significance level α = 0.05, the critical value for a one-tailed test is Zα = 1.645 (from the standard normal distribution table).

The effect size δ can be calculated as the difference between the true average (μa) and the hypothesized average (μ0), divided by the standard deviation (σ):

δ = (μa - μ0) / σ

Since we know the power, significance level, effect size, and standard deviation, we can solve for the sample size using the equation above.