Question

According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $56,907. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,507. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 240 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 240 nurses is found to be $57,100.932. Completely describe the sampling distribution of the sample mean salary when samples of size 240 are selected. mean: μ ¯ y = standard deviation: σ ¯ y = (round your answer to 4 decimal places) shape: the distribution of ¯ y is because What conjecture has been made? The mean salary for registered nurses in Ohio is greater than $57,100.932. The mean salary for registered nurses in Ohio is $56,907. The mean salary for registered nurses in Ohio is greater than $56,907. The mean salary for registered nurses in Ohio is $57,100.932. Using the distribution described in part a, what is the probability of observing a sample mean of 57,100.932 or more? z = (round to 2 decimal places) probability = (include 4 decimal places) Based on the probability found, what conclusion can be reached? The probability would be classified as . So, there evidence to support the conjecture that the mean salary for registered nurses in Ohio is greater than $56,907.

Answer 1

mean: μ ¯ y = $56,907

σ ¯ y = 5507/√240 =355.4753

shape: approximately normal since sample size is greater than 30

The mean salary for registered nurses in Ohio is $56,907.

probability of observing a sample mean of 57,100.932 or more:

z score =(57100.932-56907)/355.4753 =0.54

probability =0.2946

The probability would be classified as usual

So, there is not evidence to support the conjecture that the mean salary for registered nurses in Ohio is greater than $56,907.