Question

For this discussion post, we are going to run a hypothesis test using the Z-distribution. Read the following: The average salary for a registered nurse in Las Vegas is claimed to be $82,000 with a standard deviation of $14,500. To determine if this information is accurate, we sampled 80 registered nurses working in Las Vegas and find their average salary to be $85,025. Test this at the α = 0.05 level.

Answer 1

The question involves conducting a hypothesis test using Z-distribution to determine the accuracy of the claimed average salary for registered nurses in Las Vegas, by comparing a sample mean to the population mean with a set significance level.

Step-by-step explanation:

The subject of this question is conducting a hypothesis test using the Z-distribution to determine if the average salary of registered nurses in Las Vegas is indeed $82,000 as claimed.

We test the null hypothesis that the population mean salary is $82,000 against the alternative hypothesis that it is different, based on the sample mean salary of $85,025 obtained from 80 nurses.

With an alpha level of 0.05, we calculate the Z-score, compare it to the critical Z-value from the Z-distribution table, and decide whether to reject the null hypothesis. The necessary computation can also include finding the standard error of the mean salary given that the population standard deviation is $14,500.