Question

According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $55,599. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,987. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 269 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 269 nurses is found to be $55,938.586.

1. Completely describe the sampling distribution of the sample mean salary when samples of size 269 are selected.
   • mean: μ¯yμy¯ =
   • standard deviation: σ¯yσy¯  =   (round your answer to 4 decimal places)
   • shape: the distribution of ¯yy¯ is Select an answer normally distributed not normally distributed  because Select an answer the sample size is large the sample size is not large the population of salaries is normally distributed the population of salaries is not normally distributed
2. What conjecture has been made?
   • The mean salary for registered nurses in Ohio is $55,938.586.
   • The mean salary for registered nurses in Ohio is greater than $55,938.586.
   • The mean salary for registered nurses in Ohio is $55,599.
   • The mean salary for registered nurses in Ohio is greater than $55,599.
3. Using the distribution described in part a, what is the probability of observing a sample mean of 55,938.586 or more?
   • z =   (round to 2 decimal places)
   • probability =  (include 4 decimal places)
4. Based on the probability found, what conclusion can be reached?
   • The probability would be classified as Select an answer large small  . So, there Select an answer is is not   evidence to support the conjecture that the mean salary for registered nurses in Ohio is greater than $55,599.

Answer 1

Ans:

Sampling distribution of y-bar

mean =55599

standard deviation=5987/sqrt(269)=365.0338  

shape: the distribution of y-bar is normally distributed because the sample size is large the population of salaries is normally distributed

The mean salary for registered nurses in Ohio is greater than $55,599.

Test statistic:

z=(55938.586-55599)/(5987/sqrt(269))

z=0.93

Probability=P(z>0.930)=0.1762

The probability would be classified as large . So, there is not   evidence to support the conjecture that the mean salary for registered nurses in Ohio is greater than $55,599.