The trends in international mathematic and science study (TIMSS) in 2007 examined eighth grade proficiency in math and science. The mean mathematics scale score for the sample of eighth grade students in the US was 508.5 with a standard error of 2.83. Construct a 95% confidence interval for the mean mathematics score for all eighth grade students in the US.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.025) and its Z score = 1.96.
95% = mean ± 1.96 SEm
To construct a confidence interval for the mean mathematics score for all eighth grade students in the US, we can use the formula:
Confidence Interval = Mean ± (Critical Value * Standard Error)
Step 1: Find the Critical Value
Since we want a 95% confidence interval, we need to find the critical value corresponding to a 95% confidence level. For a normal distribution, this is typically 1.96.
Step 2: Calculate the Margin of Error
The Margin of Error is the product of the critical value and the standard error.
Margin of Error = Critical Value * Standard Error
Step 3: Calculate the Confidence Interval
The Confidence Interval is calculated by adding and subtracting the Margin of Error from the mean.
Confidence Interval = Mean ± Margin of Error
Given values:
Mean (μ) = 508.5
Standard Error (SE) = 2.83
Critical Value (CV) = 1.96 (for a 95% confidence level)
Calculations:
Margin of Error = CV * SE = 1.96 * 2.83 ≈ 5.545
Confidence Interval = 508.5 ± 5.545
Therefore, the 95% confidence interval for the mean mathematics score for all eighth grade students in the US is approximately (502.955, 514.045).