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.

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

The formula for the confidence interval is:

Confidence Interval = sample mean ± (critical value * standard error)

First, let's calculate the standard error, which represents the accuracy of the sample mean as an estimate of the population mean. The standard error is calculated using the formula:

Standard Error = standard deviation / (√sample size)

In this case, the standard deviation is 4 and the sample size is 64. Plugging these values into the formula:

Standard Error = 4 / √64 = 4 / 8 = 0.5

Next, we need to find the critical value, which corresponds to the desired confidence level. For a 95% confidence level, the critical value can be found using a statistical table (such as the Z-table) or using a calculator. For simplicity, let's assume that the critical value for a 95% confidence level is 1.96, which is a commonly used value.

Now we can plug the values into the confidence interval formula:

Confidence Interval = 28 ± (1.96 * 0.5)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 28 + (1.96 * 0.5) = 28 + 0.98 = 28.98

Lower bound = 28 - (1.96 * 0.5) = 28 - 0.98 = 27.02

Therefore, the estimated mean mathematics ACT score for all statistics students at the college is 28, with a 95% confidence interval ranging from 27.02 to 28.98.