Name
Student ID #
Class Section
Instructor
Math 1070
Spring 2011
EXAM
Dept. Use Only
Exam Scores
Problem Points
1.
15
2.
20
3.
10
4.
15
5.
15
6.
15
7 or 8.
10
TOTAL
Score
Show all your work and make sure you justify all your
answers.
Math 1070
Exam
1. The daily study times of students follows a normal distribution with
unknow mean µ, and a standard deviation of 25 minutes. A random
sample of 100 students is taken and it is found that X̄ = 130.
(a) Find a 99% confidence interval for the the mean study time µ.
(b) Suppose that you want a specified margin of error of 10 minutes
in your confidence interval. What must your sample size be to
achieve this margin of error?
(c) Students claim to study 120 minutes per day. Test the hypothesis
that H0 µ = 120 against the alternative that HA µ 6= 120 at the
5% significance level.
1
2. The number of text messages send by a person follows a normal distribution with unknown mean and standard deviation. A random sample
of 100 individuals is taken. It is found that X̄ = 6, and S = 3.
(a) Find a 99% confidence interval for the the mean number of text
messages µ.
(b) Your friend claims that the mean number of text messages on
only 5 per day. Test the hypothesis that H0 µ = 5 against the
alternative that HA µ < 5 at the 5% significance level.
2
3. The average life expectancy of a large breed of dog is found to be
X̄L = 10, and SL = 4. The average life expectancy of a small breed of
dog is found to be X̄s = 12, and Ss = 1.5.
(a) Find a 95% confidence interval for the mean differences in life
expectancy µL − µs .
(b) Test the hypothesis that H0 µL = µs against the alternative that
HA µL 6= µs at the 5% significance level.
3
4. Lactose intolerance causes difficulty digesting diary products that contain lactose. It is particularly common among people of Aferican and
Asian descent. In the united states 82% of the population is white,
14% is black, and 4% is Asian. Moreover 15% of whites, 70% of blacks,
and 90% of Asians are lactose intolerant.
(a) What percent of the entire population is lactose intolerant?
(b) What percent of people who are lactose intolerant are Asian?
4
5. Consider the experiment of tossing two regular dice. Let A be the event
that the sum of face values of the two dice is a 10, and B the event
that die one rolls a 6 and die 2 rolls a 4.
(a) Are the events A and B independent?
(b) What is the probability of A given B?
5
(c) What is the probability of A or B?
6