Problem 1. (6 points) Calculate the area under the Normal curve for the following values
of X, when the mean is 100 and the standard deviation is 20.
(a.) P(X>140)
(b.) P(130<X<140)
Problem 2. (10 points) The following table includes the average number of runs scored
in American League and National League baseball stadiums for the first half of
the 2001 season.
American
National
11.1 10.8 10.8 10.3 10.3 10.1 10.0 14.0 11.6 10.4 10.3 10.2 9.5 9.5
9.5 9.4 9.3 9.2 9.2 9.0 8.3
9.5 9.5 9.1 8.8 8.4 8.3 8.2 8.1 7.9
(a.) Do a box plot for each league.
(b.) Find the mean and standard deviation for each league.
Problem 3. (10 points) The following table shows the number of live births per 1000
women aged 15-44 years in the United States, starting in 1965.
Year
65
70
75
80
85
90
95
Rate
19.4
18.4
14.8
15.9
15.6
16.4
14.8
(a.) Draw a scatterplot for this data.
(b.)Find the equation for the regression line that best fits these data and give the
correlation.
(c.) Interpret the meaning of the slope of the regression line in terms of live births
and time.
(d.)What does the regression line predict for birth rate in 2012?
Problem 4. (10 points) The maker of a portable phone claims that the phone has a range
of 150 feet with a standard deviation of 12. A customer found that the range for
her phone was only 130, so she returned the phone saying that either the
advertised range was incorrect or there was something wrong with her phone.
(a.) What null hypothesis would you use to test the customer’s statement? What is
the p-value? What conclusion can you draw from this?
(b.) An independent research company tests 36 phones and finds that the average
range is 140. Does this show that the company claim is incorrect? What is the
null hypothesis? What is the p-value?
Problem 5. (4 points) Recent studies have shown that Vioxx, a drug for arthritis, causes
heart attacks. In earlier testing, the makers of this drug declared that it was safe.
What kind of error did the researchers make when testing whether or not the drug
resulted in more than the average number of heart attacks? Explain.
Problem 6. (4 points) Circle all that apply. The distribution of sample means has…
(a.) A mean equal to the population mean and a standard deviation equal to the
population standard deviation.
(b.) A normal distribution that is more spread out than the population distribution.
(c.) A standard deviation that increases with the sample size.
(d.) A normal distribution with a standard deviation that depends on sample size.
Problem 7. (10 points) Statistics indicate that 3% of all births produce twins. Data from a
large city hospital found 20 sets of twins born to 469 teenage girls.
(a.) Some of the doctors have suggested that these young women have twins more
frequently than most women. If you wanted to test this, what would be the null
hypothesis?
(b.) Test this hypothesis, what is the p-value and what conclusion can you draw from
this?
(c.) Find a 95% confidence interval for the sample value of the proportion p (20 in
469).
Problem 8. (4 points) The probability of passing a test is 0.76 at a particular school.
Suppose we randomly select a class of 10 students from this school. The following
questions deal with this class of 10 students.
(a.) What is the mean for the distribution of the proportion of students passing?
What is the standard deviation for the proportion?
(b.)What is the mean for the number of students passing? What is the standard
deviation?
(c.) What is the probability of exactly 3 students passing?
Problem 9. (2 points) A 95% confidence interval for a population mean is .
(a.) Can you reject the null hypothesis that at the 5% significance level? Why or
why not?
(b.)Can you reject the null hypothesis that at the 5% significance level? Why or
why not?
Problem 10. (10 points) Kellogg’s Froot Loop cereal comes in six fruit flavor: orange,
lemon, cherry, raspberry, blueberry, and lime. Hazel poured out her morning bowl
of cereal and methodically counted the number of cereal pieces of each flavor.
Here are her data:
Flavor:
Orange
Lemon
Count:
28
21
Cherry
16
Raspberry
25
Blueberry
14
Lime
16
Test the null hypothesis that the population of Froot Loops produced by Kellogg’s
contains an equal proportion of each flavor. If you find a significant result,
perform a follow-up analysis.
Problem 11. (10 points) Aspirin prevents blood from clotting and so helps prevent
strokes. The Second European Stroke Study asked whether adding another
anticlotting drug name dipyridamole would be more effective for patients who
had already had a stroke. Here are the data on strokes during the two years of the
study:
Group
1
2
Treatment
Placebo
Aspirin
Number of Patients Number of strokes
1649
250
1649
206
3
4
Dipyridamole
Both
1654
1650
211
157
Do the data provide convincing evidence of the difference in the effectiveness of the four
treatments? Carry out an appropriate test at the significance level.
