STA 2023 Honors
Spring 2007 Exam 1
Name ___________________________________
UF ID# ___________________
1. The following is a list of coffees and their grams of caffeine per 8 oz serving.
Coffees
General Foods International Coffee, Viennese Chocolate Cafe
Maxwell House Cappuccino, Amaretto
Caf/serving
26
27
Maxwell House Cappuccino, French Vanilla or Irish Cream
General Foods International Coffee, Swiss Mocha
Maxwell House Cappuccino, Mocha
General Foods International Coffee, Cafe Vienna
Coffee, instant
47
55
63
90
95
102
135
General Foods International Coffee, Orange Cappuccino
Coffee, brewed a) Find the mean and standard deviation. b) Find the Five Number Summary. c) Construct the boxplot for the amount of caffeine per serving for those different types of coffee in the plot given below (left).
Boxplot of caf/serving vs type Boxplot of caf/oz vs type
140 18
120
100
80
60
16
14
12
10
8
6
4
40
2
20
0 brewed tea caf waters coffee type iced tea soft drinks brewed tea caf waters coffee type iced tea soft drinks d) Briefly describe the two sets of boxplots above that compare the distribution of caffeine per serving and caffeine per ounce of different types of beverages: brewed tea, caffeinated water, coffee, iced tea and soft drinks. Which type of beverage has the biggest serving size?

2. Is there any relationship between a country’s fertility rate and its Gross Domestic Product
(GDP)? Fertility rate is defined and the mean number of children per adult woman in that country. GDP is a measure of the country’s economy, and is measured in thousands of US dollars, per person. The plot of the data and some summary statistics appear below.
Scatterplot of GDP vs FERTILITY
35
30
Mean Stdev
GDP 15.99 10.6
25
20
Fertility 2.379 1.245
R
2
= 37.8%
15
10
5
0
1 2 3 4
FERTILITY
5 6 7 a) Find the correlation, and interpret it. b) Find the Least Squares Regression Equation to predict y=GDP from x=Fertility Rate. c) Plot the regression line on the scatterplot above. d) Interpret the slope and intercept, if appropriate. If not appropriate, explain why not. e) Interpret R 2 . f) One of the countries in the study was Saudi Arabia, with a GDP of 13.33 and a
Fertility Rate of 4.5. Find the residual for this point and interpret.

3. Total cholesterol levels of postmenopausal women are approximately Normal, with a mean of 220 and a standard deviation of 40. a) What percentage of these women have a total cholesterol level of 240 or above – what is considered a high risk for heart disease? b) What cholesterol level would place one of these women in the top 3% of the distribution?
4. In a jury trial, supposed the probability the defendant is convicted, given guilt, is 0.95, and the probability the defendant is acquitted, given innocence, is also 0.95. Suppose that
90% of all defendants truly are guilty. a) Given the defendant is convicted, find the probability that he or she was actually innocent. Use the table below to find this probability.
Innocent Guilty
Convicted
Acquitted b) If there are a thousand trials in a year in one city (and the conditions described above apply), approximately how many innocent defendants will be convicted?

5. According to a recent study, 80% of brides in the US take the surname of their new husband. Suppose we randomly sample 10 recently recorded marriages in City Hall and count X= the number of those brides changed their surname. a) What is the probability distribution of X? b) Find the mean and standard deviation of the distribution of X. c) Find the probability that at least one of those 10 brides kept her own surname. d) Find the probability that exactly 6 of those 10 brides changed their surname.
6. Use the Empirical Rule to explain why the standard deviation of a bell-shaped distribution for a large data set is often roughly estimated by s = range/6. e) How would things change in the problem above if instead of 10 random marriages from City Hall we used the 10 marriages announced in the alumni newsletter for the
UF Law School?