Final answer:
- a. To calculate the sample proportion, divide the number of samples that have pulled an all-nighter by the total number of samples. In this case, if we have 100 samples and 20 students have pulled an all-nighter, the sample proportion is 20/100 = 0.2 or 20%..
- b. The confidence interval at a 95% confidence level represents a range of values within which the true population proportion is likely to fall. It provides a measure of uncertainty. The confidence interval can be interpreted as follows: We are 95% confident that the true proportion of students who have pulled an all-nighter this semester is between the lower bound and upper bound of the confidence interval.
- c. The margin of error represents the maximum amount of error that is allowed in the estimate. To determine the margin of error, multiply the critical value (obtained from the t-distribution table or calculator) by the standard error. The margin of error gives us an idea of the precision of the estimate.
- d. To calculate the population mean, you need to find the sum of all the values in the population and divide it by the total number of values in the population.
Step-by-step explanation:
To estimate the sample proportion, divide the number of students who have pulled an all-nighter by the total number of samples. In this case, the number of students who have pulled an all-nighter can't be determined from the information given.
The confidence interval represents the range in which the true proportion of students who have pulled an all-nighter is likely to fall. It is calculated as the point estimate plus or minus the margin of error. The margin of error is found by multiplying the critical value (obtained from a t-distribution table) by the standard error of the proportion.