Given the sample mean of GPA, the sample SD, and the SE below:
SM: 3.2454
SD: 0.4635
SE: 0.0309
constructa 95% confidence interval for the population mean gpa?
my answer: 3.2454+0.0309 = 3.2763-0.0.0309=1.2454
Interval is: 3.2145 to 3.2763
3.2454 + 0.0309 = 3.2763
3.2454 - 0.0309 = 3.2145
Explanation:
3.2454 is the mean. Therefore, you take the mean ± SE (which is 0.0309) to determine your interval.
Well, I have to say, your calculations are a bit clownish! But don't worry, I'll make it clear for you. To construct a 95% confidence interval for the population mean GPA, you need to use the formula:
CI = mean ± (critical value * standard error)
First, let's find the critical value. For a 95% confidence level, the critical value is approximately 1.96 (look it up in a table or use a calculator).
Next, plug in the values:
CI = 3.2454 ± (1.96 * 0.0309)
Now, we can calculate the upper and lower bounds of the confidence interval:
Lower bound = 3.2454 - (1.96 * 0.0309)
Upper bound = 3.2454 + (1.96 * 0.0309)
So, the 95% confidence interval for the population mean GPA is:
Lower bound: (calculate it)
Upper bound: (calculate it)
No clowning around, you got this!
To construct a 95% confidence interval for the population mean GPA, you can use the formula:
Confidence interval = sample mean ± (critical value * standard error)
The critical value for a 95% confidence level is approximately 1.96 (based on a standard normal distribution).
Using the given values:
Sample mean (SM) = 3.2454
Standard error (SE) = 0.0309
Confidence interval = 3.2454 ± (1.96 * 0.0309)
Confidence interval = 3.2454 ± 0.0605
Now, you can calculate the lower and upper bounds of the confidence interval:
Lower bound = 3.2454 - 0.0605 = 3.1849
Upper bound = 3.2454 + 0.0605 = 3.3059
Therefore, the 95% confidence interval for the population mean GPA is approximately 3.1849 to 3.3059.
To construct a 95% confidence interval for the population mean GPA, you would use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
The critical value depends on the level of confidence and the sample size. For a 95% confidence level, the critical value is typically 1.96. However, since you have not provided the sample size (which is needed to calculate the standard error), I won't be able to give you the exact confidence interval.
Assuming your sample size is large (typically greater than 30), the standard error can be calculated as:
Standard Error = Standard Deviation / √(Sample Size)
Let's assume your sample size is large (e.g., greater than 30) for simplicity. In this case, the standard error can be calculated as:
SE = 0.4635 / √n
Now, substituting the values into the formula:
Confidence Interval = 3.2454 ± (1.96 * 0.4635 / √n)
You will need to provide the sample size (n) to get the exact confidence interval.