Given the sample mean of GPA, the sample SD, and the SE below:
SM: 3.2454
SD: 0.4635
SE: 0.0309
construct a 68% confidence interval for the population mean gpa
My answer is: 0.4635 to 3.7089
68% = mean ± .995 SEm = 3.2454 ± .995(.0309)?
.995(.0309) = .0307455
3.2146545 to 3.2761455
I'm not sure what SD and SE symbolize.
Standard Deviation
Standard Error
THESE ARE WRONG
Well, you certainly went the extra mile with your answer! However, it seems like you might have mixed up some things along the way. Let me help you out with the correct 68% confidence interval.
Since you have the sample mean (SM) and the standard error (SE), we can construct the confidence interval by taking the sample mean and adding/subtracting the margin of error.
The margin of error is determined by multiplying the SE by the appropriate z-score for the desired confidence level. For a 68% confidence level, the z-score is approximately 1 (simplifying things a bit here).
So, the margin of error would be 1 * 0.0309 = 0.0309.
Now, we can construct the confidence interval by adding/subtracting the margin of error to/from the sample mean:
Lower bound: SM - margin of error = 3.2454 - 0.0309 = 3.2145
Upper bound: SM + margin of error = 3.2454 + 0.0309 = 3.2763
Therefore, the correct 68% confidence interval for the population mean GPA would be approximately 3.2145 to 3.2763.
Hope that helps!
To construct a confidence interval for the population mean GPA, we can use the formula:
Confidence Interval = Sample Mean ± (Z * Standard Error)
The Z value represents the number of standard deviations from the mean that corresponds to the desired confidence level. For a 68% confidence level, we use Z = 1.
Let's calculate the confidence interval step by step:
Step 1: Calculate the margin of error. The margin of error is equal to Z multiplied by the standard error.
Margin of Error = Z * SE = 1 * 0.0309 = 0.0309
Step 2: Calculate the lower and upper bounds of the confidence interval. The lower bound is obtained by subtracting the margin of error from the sample mean, and the upper bound is obtained by adding the margin of error to the sample mean.
Lower Bound = Sample Mean - Margin of Error = 3.2454 - 0.0309 = 3.2145
Upper Bound = Sample Mean + Margin of Error = 3.2454 + 0.0309 = 3.2763
Therefore, the 68% confidence interval for the population mean GPA is 3.2145 to 3.2763.
It appears that the answer you provided, 0.4635 to 3.7089, is not correct. Please double-check your calculations and ensure you are using the correct formula for constructing a confidence interval.