Question

answer 5a-c

You want to know the average number of pushups that a college student can do in two minutes. You hang out at the HUB and ask random people walking by to see how many pushups they can do in 2 minutes. The first 5 people who agree to participate do the following number of pushups: 52, 65, 44, 71, and 58. Assume that those people represent a random sample of college students, then make the following calculations. a) (5 points) What is an unbiased estimate of the average number of pushups done by the population of college students? b) (5 points) What is the variance of this sample? (Note: Be sure to clearly show your work here, in case you are using an incorrect number from above.) c) (10 points) Calculate a 90% confidence interval for the average number of pushups that a college student can do. (Note: Be sure to clearly show your work here, in case you are using an incorrect number from above.)

Answer 1

X	∑x²
52	2704
65	4225
44	1936
71	5041
58	3364

∑x = 290

∑x² = 17270

n = 5

a) Unbiased estimate of average, x̅ = Ʃx/n = 290/5 = 58

b) Variance, s² = (Ʃx² - (Ʃx)²/n)/(n-1) = (17270-(290)²/5)/(5-1) = 112.50

c) 90% Confidence interval :  

At α = 0.10 and df = n-1 = 4, two tailed critical value, t-crit = T.INV.2T(0.10, 4) = 2.132

Lower Bound = x̅ - t-crit*√(s²/n) = 58 - 2.132 * √(112.5/5) = 47.888

Upper Bound = x̅ + t-crit*√(s²/n) = 58 + 2.132 * √(112.5/5) = 68.112

47.888 < µ < 68.112