7. Give and interpret the 95% confidence interval for the hours of sleep a student gets
Formula for 95% confidence interval using a z-table:
CI95 = mean ± 1.96(sd/√n)
I hope this will help.
To calculate the 95% confidence interval for the hours of sleep a student gets, you would need a sample of data on sleep hours from a group of students. Here is a step-by-step guide on how to calculate and interpret the confidence interval:
1. Gather the data: Collect the number of hours of sleep each student in the sample gets. Ensure that the sample is representative of the population you want to make inferences about.
2. Calculate the sample mean: Add up all the sleep hours in the sample and divide by the total number of students. This will give you the average number of sleep hours.
3. Determine the sample standard deviation: Calculate the standard deviation of the sleep hours in the sample. This measures the variability or spread of the data around the mean.
4. Determine the sample size: Count the number of students in the sample. This will be used to determine the appropriate critical value from the t-distribution.
5. Calculate the standard error: Divide the sample standard deviation by the square root of the sample size to find the standard error. This will provide an estimate of the standard deviation of the population mean.
6. Find the critical value: Using a t-distribution table or a statistical calculator, find the critical value associated with a 95% confidence level and the degrees of freedom (sample size minus one).
7. Calculate the margin of error: Multiply the standard error by the critical value obtained in the previous step. This will give you the margin of error.
8. Calculate the lower and upper bounds: Subtract the margin of error from the sample mean to get the lower bound, and add the margin of error to the sample mean to get the upper bound. These two values define the confidence interval.
9. Interpret the confidence interval: A 95% confidence interval means that if we were to repeat this sampling process multiple times, we would expect the true mean hours of sleep to fall within this range about 95% of the time. For example, if the 95% confidence interval is (6.5, 7.3) hours, we can say with 95% confidence that the average number of hours of sleep a student gets is between 6.5 and 7.3 hours.
It is important to note that the interpretation of the confidence interval assumes that the data follows a normal distribution and that the sampling process is random.