Suppose we divide the patients according to whether or not they received antibiotics, and calculate the
mean and standard deviation for each of the two subsamples:
answers:
x, s, n x sd n
Antibiotics 11.57, 8.81, 7
No antibiotics 7.44, 3.70, 18
interpretation:
It appears that antibiotic users stay longer in the hospital.
help,
I understand how to get the answers given the set of data using the formula, but i don't understand the interpretation. Thank you
sorry...it should say
x, s, n
x=mean
s=standard deviation
n=number of patients
Is this what you have done?
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. How does that relate to your level of significance? If the probability is smaller and your mean is for length of hospital stays, the interpretation is correct.
However, I do not see any control for severity of the illness. More severe disorders would probably require antibiotics and longer stays.
The interpretation of the data given is that patients who received antibiotics stayed longer in the hospital compared to patients who did not receive antibiotics.
To understand this interpretation, let's look at the data provided:
- For the patients who received antibiotics:
- The mean (x) is 11.57, which means that on average, they stayed in the hospital for approximately 11.57 units (the specific unit is not provided in the question).
- The standard deviation (sd) is 8.81, which indicates the amount of variation in the lengths of stay among this group.
- The sample size (n) is 7, meaning there were 7 patients in this group.
- For the patients who did not receive antibiotics:
- The mean (x) is 7.44, showing that, on average, they stayed for approximately 7.44 units in the hospital.
- The standard deviation (sd) is 3.70, indicating that there is less variation in the lengths of stay among this group compared to the antibiotic group.
- The sample size (n) is 18, meaning there were 18 patients in this group.
Based on this information, we can see that the mean length of stay for patients who received antibiotics is higher (11.57) than for those who did not receive antibiotics (7.44). This suggests that, on average, patients who were given antibiotics had a longer stay in the hospital.
However, it is important to keep in mind that this interpretation is based solely on the provided data. To draw more reliable conclusions, additional factors such as the severity of the patients' conditions, the specific medications administered, and other relevant variables should be considered.