1.) A recent study by Educator Magazine was conducted to determine the amount of time students spend on homework. A random sample of 30 students were asked for the number of hours they spend doing homework every night. This gave a sample mean of 3.7 hours with sample standard deviation 1.5 hours. a.) Find the point estimate for the population mean (i. e. sample mean).

b.) Find the standard deviation of the sample.

c.) Find the sample size.

d.) Find the margin of error for a 95% confidence interval.

e.) Find a 95% confidence interval.

F. Which of the following are correct interpretation(s) of the interval from part (d)? (Highlight your response)

a. 95% of the students in the sample will spend the number of hours doing homework based on the computed confidence interval.

b. 95% confident the sample mean for the number of student homework hours every night is within the calculated confidence interval.

c. 95% confident that the true population mean for the number of student homework hours every night is within the calculated confidence interval.

d. 95% of the student population will spend the number of hours doing homework based on the computed confidence interval.

G. After having constructed the confidence interval in the first part of the problem, you are dissatisfied with its size. Which of the following are acceptable ways to decrease the width of the confidence interval? (Highlight your response)

a. Decrease the confidence level.
b. Increase the confidence level.
c. Decrease the sample size.
d. Increase the sample size.
e. (a) or (d)
f. (b) or (c)

The average monthly cell phone bill was reported to be $50 by the U. S. Wireless Industry in 2010. A recent sample from a large cell phone company found the following monthly cell phone charges (in dollars) from ten of their customers:

55.83, 49.88, 62.98, 70.42, 60.47, 52.45, 49.20, 50.02, 58.60, 51.29

a.) Find the point estimate for the population mean (i. e. sample mean).

b.) Find the standard deviation of the sample.

c.) Find the sample size.

d.) Find the margin of error for a 99% confidence interval.

e.) Find a 99% confidence interval for the mean number of hours all students spend working on homework.

f.) Interpret the confidence interval.

g.) Based on your confidence interval, is there evidence that the average phone bill has increased from $50?