Given the sample mean of GPA, the sample SD, and the SE below:
SM: 3.2454
SD: 0.4635
SE: 0.0309
construct a 99.7% confidence interval for the population mean gpa.
My answer: 3.2145 to 9.6435
99.7% = mean ± 2.965 SEm
I am confused --- so the correct answer is 2.965 or do I have to +, - from 3.2454 to get a range?
this answer is wrong
To construct a confidence interval for the population mean GPA, we will use the sample mean (SM) and the standard error (SE). The formula for a confidence interval is:
Confidence Interval = sample mean ± (critical value * standard error)
Since you want a 99.7% confidence interval, we need to find the corresponding critical value. The critical value can be obtained from the z-table or by using a statistical calculator.
In this case, a 99.7% confidence interval corresponds to a z-score of 3. In other words, the critical value is 3.
Now, let's calculate the confidence interval:
Lower Bound = sample mean - (critical value * standard error)
Upper Bound = sample mean + (critical value * standard error)
Lower Bound = 3.2454 - (3 * 0.0309)
Lower Bound = 3.2454 - 0.0927
Lower Bound = 3.1527
Upper Bound = 3.2454 + (3 * 0.0309)
Upper Bound = 3.2454 + 0.0927
Upper Bound = 3.3381
Therefore, the 99.7% confidence interval for the population mean GPA is approximately 3.1527 to 3.3381.