Discussion:
Q1. The heights of a random sample of 50 college students showed a mean of 174.5 cm and standard deviation of 6.9 cm.
a) Construct a 98% confidence interval for the mean height of all college students.
b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 cm?
Q2. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hrs. A sample of 30 bulbs has an average life of 780 hrs. How large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hr of the true mean?
Q3. A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calories is approximately normal.
Q4. Consider E(S'2) = E[(n-1/n)S2] = (n-1/n)*E(S2) = (n-1/n)o2 and S'2, the estimator of o2. Analysts often use S'2
a) What is the bias of S'2?
b) Show that the bias of S'2 approaches zero as n infinity.