Question

Pretty Problem #6 (Confidence Intervals) There is a general consensus that a person's height is about the same as their wingspan. That is to say, if you calculate “Ape Index” (wingspan minus height in inches) we should get zero on average for a whole population of people. Since Rachael has super short arms (ape index of -3) and all her "friends” "lovingly” call her “t-rex arms” Rachael would like to think that she's not alone in the t-rex department and that actually the average Ape Index is a negative number for the general population and that in fact it is her “friend” and coworker Ross Geller who is the super weirdo with his long “sloth” arms and his ape index of +3. Over the last several semesters, she has had her statistics students calculate their Ape index, here are their results: 366 students with an average ape index of -1.1850 inches and a sample standard deviation of 2.8016 inches. A. Use the sample data to give a 95% confidence interval to estimate the Average Ape Index. Identify what software you are using to give the interval. B. Clearly describe what the range of values from your confidence interval represents in plain language. C. What would you say to someone who, like Rachaell, has a – 3 ape index? How about to someone like Ross Geller with a +3 ape index?

Answer 1

A) We shall be using excel here

Since the sample is large enough we shall use Z distribution to calculate the confidence interval of the popuation mean.

A B с D E 1 - 1.185 2.8016 2 Sample mean 3 S.Dev. 4 n 5 Z critical 6 standard error 7 Margin of error 8 9 Lower limit 10 Upper Limit 11 366 1.9600 0.1464 0.2870 .-NORM.S.INV(0.025) B3/SQRT(B4) B5*B6 -1.4720 B2-B7 -0.8980 B2+B7 12

B) We are 95% confident that the population average Ape index will lie within the values calculated above which is (-1.4720 in ,-0.8980 in )

C) Both Rachael and Ross Geller have ape index which is outside the limits of the confidence interval calculated above.

Values that are outside the 95% confidence interval are unlikely to be the true value.