7. Give and interpret the 95% confidence interval for the hours of sleep a student gets.

95% CI = (6.21, 7.69)

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To determine the 95% confidence interval for the hours of sleep a student gets, you would need data on the hours of sleep obtained from a sample of students. Here's how you can calculate and interpret it:

1. Gather data: Collect the hours of sleep data from a representative sample of students. Make sure the sample size is large enough to meet the assumptions for a confidence interval calculation.

2. Calculate the sample mean: Find the average hours of sleep for the sample.

3. Determine the standard deviation: Calculate the standard deviation of the sample data. This will provide a measure of variability in the hours of sleep.

4. Calculate the standard error: Divide the standard deviation by the square root of the sample size to obtain the standard error. The standard error estimates the variability of the sample mean.

5. Find the critical value: Look up the critical value associated with a 95% confidence level in the appropriate statistical table or use a calculator. For a normal distribution, the critical value is approximately 1.96.

6. Calculate the margin of error: Multiply the critical value by the standard error to establish the margin of error. The margin of error represents the amount of uncertainty in the confidence interval.

7. Calculate the lower and upper bounds: Subtract the margin of error from the sample mean to find the lower bound, and add it to the sample mean to find the upper bound.

8. Interpret the confidence interval: The 95% confidence interval for the hours of sleep a student gets is estimated to be between the lower bound and the upper bound. This means that we are 95% confident that the true population mean for the hours of sleep falls within this range. It is important to note that this interval does not imply that each individual student will fall within this range, but rather that the population mean is likely to fall within it.

By following these steps, you can calculate a 95% confidence interval for the hours of sleep a student gets and interpret its meaning.