A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

To estimate the mean mathematics ACT score for all statistics students at the college and calculate the 95% confidence interval, we can use the formula for the confidence interval:

CI = X̄ ± (Z * (σ/√n))

Where:
- CI represents the confidence interval
- X̄ is the sample mean
- Z is the Z-score for the desired confidence level
- σ is the population standard deviation (given as 4)
- n is the sample size (given as 64)

First, we need to find the Z-score for a 95% confidence level. The Z-score can be obtained using statistical tables or with the help of statistical software. For a 95% confidence level, the Z-score is approximately 1.96.

Next, we substitute the given values into the formula:

CI = 28 ± (1.96 * (4 / √64))

Calculating the expression within the parentheses:

CI = 28 ± (1.96 * 0.5)

Now we can calculate the upper and lower limits of the confidence interval:

Upper limit = 28 + (1.96 * 0.5)
Lower limit = 28 - (1.96 * 0.5)

Simplifying the calculations:

Upper limit = 28 + 0.98
Lower limit = 28 - 0.98

Which gives us:

Upper limit = 28.98
Lower limit = 27.02

Therefore, the 95% confidence interval for the mean mathematics ACT score for all statistics students at this college is (27.02, 28.98).

95% = mean ± 1.96 SEm

SEm = SD/√n