Question

PART I: How many calories are there in 3 ounces of French fries? It depends on where you get them? Good Cholesterol Bad Cholesterol, by Roth and Streicher, gives the data from eight popular fast-food restaurants. Assume the data is normally distributed. The data (in calories) are 222 255 254 230 249 222 237 287 Construct the following: 99% confidence interval: __________________________ 98% confidence interval: __________________________ 95% confidence interval: __________________________ 90% confidence interval: __________________________ 85% confidence interval: __________________________ 1. As the degree of the confidence decreases, the confidence interval limits...? 2. In your own words, explain why the preceding completed statement makes sense. PART II: IQ scores are normally distributed with a mean of 100 and standard deviation of 15. A psychologist has gathered 30 samples of 12 such scores. He then entered his data into SPSS and constructed 30 confidence intervals. On the next page are the 90% confidence intervals with samples of size 12 from a normal distribution with mean 100 and standard deviation 15 in the columns labeled x1 to x30. 1. How many of the 30 confidence intervals would you expect to contain 100? 2. How many of the 30 confidence intervals actually contain 100? Highlight those that don’t on your output. 3. Would you expect the answers to questions 1) and 2) to always be exactly the same? Explain.

Answer 1

Page Date: 1 Solution. The data are given as normally distributed below. x 222 255 254 230 1x2 49284 65025 6 4516 52900 62001 49284 56169 82369 I 481548 249 222 237 287 suun 1956 sample mean x = i sxi - 1956 | X = 244.5 sample verance $? (EX= 4(XD (481548-|(1955) - 4 72. 286 472 286 s=532 = 21.732

Date: / defroe y freedom - n1 =8-1- 7 Confidence loved esterval is とマ X- tas ir s t Me X+ t ft) & at 99% t= 3.5 M = x + tas & = 244.5+ 3.5 7.68 = 244.5€ 26.888 CI (217.612, 271.388] at 98% at 95% u = x + t, Q5%) & t= 2.36 c. I = [226.332, 262.668] at 90% calculate same as - 11.89 c. [= [229.943, 259.057] at 85%, turi C1 = (233 629 255 371 = [ 233, 256