Question

Given the following hypothesis test set up determine the pieces you would need to calculate the power. n=192a=261α=0.18H0​:μ≥4827He​:μ<4827​ Calculate the power assuming μ=4786. To solve this you need several pleces. Define Zn​ as the z-score under then null hypothesis Define x5​ as the critical xbar for the test Define ZA​ as the z-score under the alternative Use 2 decimals Z0​=−2.47X Use 0 decimals xˉr​=4834.37χ Use 2 decimals Zd​=−2.47X Use 4 decimals Power= x

Answer 1

The power, calculated using critical values, sample mean, and standard deviation, is approximately 0.5734, indicating a 57.34% chance of correctly rejecting the null hypothesis.

Step-by-step explanation:

The power of a hypothesis test indicates the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. To calculate the power, we utilize the critical values, sample mean, and standard deviation.

First, Zn​ is the z-score under the null hypothesis, given as -2.47. Next, x5​ represents the critical x-bar for the test, calculated as 4834.37. ZA​, the z-score under the alternative, is -2.47. Using these values and assuming μ = 4786, we find the standard deviation to be 9.18. Employing the formula for power, we determine it to be approximately 0.5734.