Overview
Reply to 2 peers
My post:
Hypotheses
The claim states the average RN salary in Las Vegas is $82,000.
H0: μ = $82,000
H1: μ ≠ $82,000
Z‑Statistic
Sample mean = $85,025
Population SD = $14,500
n = 80
Standard error = $14,500 / √80 = 1,621.15
Z = (85,025 − 82,000) / 1,621.15 =1.866
P-value
Two‑tailed p = 2 × P(Z > 1.866) = 0.0620
Conclusion
Comparing this p-value with our level of significance p = 0.05, we observe that the value of p = 0.062 exceeds our significance level p = 0.05. Thus, we do not reject the null hypothesis. This implies that, with these statistics, we are not statistically well balanced to assert that the true average wages of the registered nurses in Las Vegas are not equal to the stated salaries of $82,000. Although the sample mean is larger, the difference cannot be considered statistically significant at the 5% level.
Other Variables & Sampling
Salaries paid to nurses could be affected by other variables that encompass the level of education, experience, certifying specialty, the type of employer, shift allowances, and union contract. In order to have an effective sample that will be representative of the population, we can apply probability-based strategies, which may be simple random sampling, stratified sampling (e.g., by hospital or specialty), or cluster sampling. Such a strategy will decrease sampling bias and promote the validity of our findings.
Peer# 1:
- What are the hypotheses based on the words given in the problem?
- The hypotheses given in the problem above is that the average salary for a registered nurse in Las Vegas in $82,000. We need to test the sample to see if the providing evidence is different or not.
- (H0: ), (H1: μ!=82,000) this shows us that it is a two tailed test because we are testing for a difference and not a direction.
- (H0: ), (H1: μ!=82,000) this shows us that it is a two tailed test because we are testing for a difference and not a direction.
- The hypotheses given in the problem above is that the average salary for a registered nurse in Las Vegas in $82,000. We need to test the sample to see if the providing evidence is different or not.
- What is our Z?
- Our Z score is 1.87
- What is the P-value?
- Since this is a two tailed test, we have to use P-value≈2x0.0307=0.0614
- Based on your p-value and alpha, what conclusion will we make? Do we have evidence that the claim is false?
- The conclusion I come to with the evidence given is that there is not enough evidence to come to a conclucion that the average salary is different than the given information of $82,000 and that the claim can not be rejected.
- Are there any other variables that could potentially impact the salary of a registered nurse? What are some methods of sampling we can use to ensure we have a representative population.
- Yes, there are many factors/variables that can change a single persons salary as a registered nurse, some examples being, years of experience, different certifications, highest level of schooling (bachelors, masters), the type of organization the hospital is which can differ the pay scale, and lastly the shift the nurse is working(morning, mid, night).
(H_0: \mu = 82,000)
(H_1: \mu \neq 82,000)Z-value:
The standard error is (14500 / \sqrt{80}), which is about 1621.78.
So,
(Z = (85025 - 82000) / 1621.78 \approx 1.87)P-value:
For a two-tailed test, the p-value is about 0.062.Conclusion:
Since the p-value is bigger than our alpha level of 0.05, we fail to reject the null hypothesis. This means we don’t have enough evidence to say the $82,000 salary claim is wrong.Other variables:
Nurse salaries can be affected by experience, education, certifications, the type of workplace, the part of Las Vegas they work in, and even what shift they work.Sampling methods:
To get a sample that actually represents the RN population, we could use simple random sampling or stratified sampling by things like hospital type or experience level. Cluster sampling could also work by randomly choosing hospitals and then sampling nurses from those locations.Supporting Resources: Hypothesis Test Basics https://www.youtube.com/watch?v=DlwOTOydeykLinks to an external site.P-Value Basics https://www.youtube.com/watch?v=KLnGOL_AUgALinks to an external site.