Final answer:
The 95% confidence interval for the difference between two population means, with a sample mean difference of 34.6 and standard deviation of 11.9, lies between 11.276 and 57.924. Option d is correct.
Step-by-step explanation:
The question you have asked pertains to constructing a 95% confidence interval for the difference between two population means based on sample data.
To determine the confidence interval, we utilize the standard deviation of the difference of the sample means and a multiplier that corresponds to the desired confidence level.
In the case of a 95% confidence interval and assuming a normal distribution, the multiplier is typically 1.96 for a Z-score.
Let's calculate the margin of error using the formula:
- Margin of Error (ME) = Z * (standard deviation of the difference)
- ME = 1.96 * 11.9
- ME = 23.324
Now, we can find the confidence interval by adding and subtracting this margin of error from the difference in sample means:
- Lower limit = 34.6 - 23.324
- Upper limit = 34.6 + 23.324
Calculating these values gives us:
- Lower limit = 11.276
- Upper limit = 57.924
Therefore, the 95% confidence interval lies between 11.276 and 57.924.
Complete question:
The difference of the sample means of two populations is 34.6, and the standard deviation of the difference of the sample means is 11.9. The 95% confidence interval lies between _____ and _____.
A. First BLANK: -11.9; Second BLANK: +11.9
B. First BLANK: -23.8; Second BLANK: +23.8
C. First BLANK: -35.7; Second BLANK: +35.7
D. First BLANK: 11.276; Second BLANK: 57.924