Suppose that a SRS of 900 12th-graders has x̅ =148. Based on this sample, a 95% confidence interval for μ is? (σ=35)

I tried using x̅ +/- z*(σ/sqrt n), so 148 +/- 1.960(35/sqrt900, but it doesn't work. What am I doing wrong?

95% = 148 ± 1.96 (35/30) =148 ± 1.96(1.17) =

148 ± 2.287 = 145.713, 150.287

Is that what you calculated?

It seems like you made a small mistake while calculating the standard error. To calculate the standard error, you need to divide the standard deviation (σ) by the square root of the sample size (n).

In this case, the sample size is 900, and the standard deviation is 35. So the correct calculation for the standard error would be:

Standard Error (SE) = σ / √n
SE = 35 / √900
SE = 35 / 30
SE = 1.1667

Now, you can use the formula for calculating the confidence interval:

Confidence Interval = x̅ ± z * SE

Since you want a 95% confidence interval, you need to find the z-value corresponding to that confidence level. For a 95% confidence interval, the z-value is approximately 1.96.

Confidence Interval = 148 ± 1.96 * 1.1667

Now you can calculate the upper and lower bounds of the confidence interval:

Upper Bound = 148 + 1.96 * 1.1667
Lower Bound = 148 - 1.96 * 1.1667

Upper Bound = 148 + 2.2867
Lower Bound = 148 - 2.2867

Upper Bound ≈ 150.2867
Lower Bound ≈ 145.7133

So, the 95% confidence interval for the population mean (μ) based on this sample is approximately (145.7133, 150.2867).

To calculate the 95% confidence interval for the population mean, you need to use the formula:

Confidence Interval = x̅ ± z * (σ / √n)

Where:
x̅ is the sample mean,
z is the z-score corresponding to the desired confidence level (in this case, 95%, which corresponds to a z-score of 1.96),
σ is the population standard deviation,
n is the sample size.

In your case, you have x̅ = 148, σ = 35, and n = 900.

Thus, the correct calculation would be:

Confidence Interval = 148 ± 1.96 * (35 / √900)

Let's compute this:

Confidence Interval = 148 ± 1.96 * (35 / 30)

Calculating further:

Confidence Interval = 148 ± 1.96 * 1.1667

Confidence Interval = 148 ± 2.2829

Therefore, the 95% confidence interval for μ is (145.7171, 150.2829).

It seems like you made an error while calculating the standard error (σ / √n). In this case, it should be (35 / √900), which simplifies to (35 / 30) ≈ 1.1667.