A large health care system gave all nurses a flat wage increase. A union representative sampled 50 nurses and found that the mean increase in total wages was 5.2% with a standard deviation of 1.61.
Using a 95% confidence interval, which statement from the union best describes the wage increase for all nurses in the system?
A) The average wage increase for nurses in the system was between 4.76% and 5.65%.
B) The average wage increase for nurses in the system was between 3.6% and 6.8%.
C) The average wage increase for nurses in the system was 5.205%.
D) The average wage increase for nurses in the system was 5.2%.
it’s a
Thumbs up if this exam is hard.
just took the exam and it is indeed A
Well, isn't this a healthy dose of statistics! Let me put on my humorous lab coat and analyze the options.
Option A) The average wage increase for nurses in the system was between 4.76% and 5.65%. Ahh, that's quite a precise range, almost like choosing between a mild flu and a moderate fever. But hey, statistically speaking, this could be a valid choice.
Option B) The average wage increase for nurses in the system was between 3.6% and 6.8%. Ah, now we're talking! This range is wider than a clown's smile, allowing for a fair amount of fluctuation. Like a seesaw, these numbers have their ups and downs, but they definitely give the union more leeway to describe the wage increase.
Option C) The average wage increase for nurses in the system was 5.205%. Oh, how precise! This answer dances on the edges of decimal places, showcasing its statistical accuracy. But hey, let's not get too caught up in the dance. After all, it's important to consider the margin of error and maintain a sense of humor.
Option D) The average wage increase for nurses in the system was 5.2%. Now, this option is as straightforward as a pancake on a plate. It takes into account the mean wage increase without involving any tricks or surprises. But remember, a confident interval does allow for some wiggle room.
Taking everything into consideration, I'd go with option B) The average wage increase for nurses in the system was between 3.6% and 6.8%. It gives the union a reasonable range to describe the wage increase, allowing for potential variation among the nurses. And as we all know, in statistics, a bit of variation is the spice of life!
To determine the most accurate statement about the wage increase for all nurses in the system using a 95% confidence interval, we can use the sample mean and standard deviation provided.
The formula for calculating a confidence interval is:
CI = X̄ ± (Z * (σ/√n))
where:
CI = Confidence Interval
X̄ = Sample Mean
Z = Z-Score (corresponding to the desired confidence level, which is 95% in this case)
σ = Population Standard Deviation
n = Sample Size
Given that the sample mean is 5.2%, the standard deviation is 1.61, and the sample size is 50, we can calculate the confidence interval.
First, we need to find the Z-Score for a 95% confidence level. A 95% confidence level corresponds to 1.96 (Z-Score) in a standard normal distribution table.
Next, we calculate the margin of error:
Margin of Error = Z * (σ/√n)
Margin of Error = 1.96 * (1.61/√50)
Margin of Error ≈ 0.449
Finally, we can calculate the confidence interval:
CI = X̄ ± Margin of Error
CI = 5.2% ± 0.449
CI ≈ 4.76% to 5.65%
Therefore, the correct statement from the union would be:
A) The average wage increase for nurses in the system was between 4.76% and 5.65%.