Download Old final 2001 without solution

I. Questions 1-4 are worth 5 points each.
1. Given the following distribution of values in a population, find  and draw the pie chart.
x
4
3
2
1
0
p(x)
0.2
0.4
0.2
0.1
0.1
2. If X has a mound-shaped, symmetric distribution with =10 and =3, then find the following
probabilities
a. Pr( X > 15)
b. Pr( X < 14)
3. What is the t-table value given
a. degrees of freedom = 17 and Pr(t > table value) = 0.05?
b. degrees of freedom = 4 and Pr(t < table value ) = 0.10?
4. Given the least squares line: yhat = 110 - 90x
a. What would be the best point estimate of y given X = 0.70 ?
Question 4 continued on the next page.
b. Plot the line on the following graph
200.0
Y
150.0
100.0
50.0
0.0
0.00
0.25
0.50
0.75
1.00
X
II. Questions 5-8 are worth 10 points each. Work any three of the four questions. DO NOT WORK ALL
FOUR IN THIS SECTION. If you work all four, I will omit question 5. You will receive full credit for
the question that you omit.
5. Suppose you are taking an exam. Someone tells you that, given how much you have studied, for each
question there is a 5% chance that you will answer it incorrectly. The exam is a twenty-question
True/False exam. Given this information, what is the chance that you will get 11 or fewer correct?
Assume the answer on one question is independent of the answer on another.
6. Suppose someone told you that they have a list of the average literacy rate of women in each country in
the world. Rather than show you the values, they tell you that the population average is 65% with a
population standard deviation of 5%. You also know that the distribution of values is highly skewed.
Given just this information
a. What percent of the countries have female literacy rates between 55% and 75%?
b. What percent of countries have female literacy rates above 50%?
7. You wish to randomly sample computers and measure their useable lifetime. You know the
population standard deviation is 6 month. How many would you have to sample to be 99% sure that
your sample mean is within 1 month of the true mean?
Formula:
Substitution:
Value:
8. A teacher creates an exam and tries it on 25 students. The sample mean is 70 with a sample standard
deviation of 15 points. If tried on all students, what would be the exam average with 90% confidence?
Assume the exam scores are normally distributed.
Formula:
Substitution:
Value:
Questions 9-12 are worth 10 points each. Work any three of the four questions. DO NOT WORK ALL
FOUR IN THIS SECTION. If you work all four, I will omit question 9. You will receive full credit for
the question that you omit.
9. You have measured the number of deaths per live births in two groups of countries (Group 1: those
with higher than 75% female literacy rate and Group 2: those with a 75% or less literacy rate). You wish
to determine if the average number of deaths per live births in Group 1 is lower than in Group 2. You
have the following information: The sample mean for Group 1is 20 and for group 2 is 70. The sample
standard deviation for group 1 is 40 , for group 2 is 20 and the sample standard deviation of the difference
in means is 4.1. Assume the sample is large enough to not worry about the lack of normality.
Complete the following:
Ho: 1 –  2 = 0
R.R. Reject Ho if t < -1.645
Ha:  1 –  2 < 0
Test Statistic formula:
Test Statistic Value:
Conclusion:
Questions 10-12 assume that you have measured the number of deaths per 1000 live births, Y, and
the literacy rate, X, for 30 countries.
10. What would be null hypothesis, the alternative hypothesis, and the rejection region for testing to
determine if increases in the female literacy rate is related to a decrease in the expected number of
deaths per 1000 live births?
Ho:
R.R. Reject Ho if
Ha:
11. With 95% confidence, for countries with a female literacy rate of 75%, what would be an
interval estimate of the average number of deaths per 1000 births? You are given that the estimated
mean number of deaths is 40 with a standard error of 30. You do not need to interpret the interval.
Formula:
Substitution:
Value:
12. In context of this problem of the number of deaths per 1000 births and the female literacy rate,
translate the following into English.
a.  y | x
b. y | x
c. 1
d. 0