110 Math 116 – 05: Test #5 (Chapters 20 – 23)
Name:
Spring 2013
Show work when possible to receive full credit for correct answers.
Give grammatically correct and clear explanations when asked to explain anything.
Problems 1 – 4 are worth 5 points each.
1. A P-value for a hypothesis test indicates:
(a) the probability that the null hypothesis is true
(b) the probability that the alternative hypothesis is true
(c) the probability of the observed statistic given that the null hypothesis is true
(d) the probability of the observed statistic given that the alternative hypothesis is true
(e) none of the above
2. A certain professor wants to see if more than 80% of her students enjoyed taking her class.
At the end of the term, she takes a random sample of students from her large class and asks,
in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses
should she test?
(a)
H 0 : p < 0.80
H a : p > 0.80
(b)
H 0 : p = 0.80
H a : p > 0.80
(d)
H 0 : p = 0.80
H a : p ¹ 0.80
(e)
H 0 : p = 0.80
H a : p < 0.80
(c)
H 0 : p > 0.80
H a : p = 0.80
3. Suppose that a manufacturer is testing one of its machines to make sure that the machine is
producing more than 97% good parts H0 : p 0.97 and Ha : p 0.97. The test results in a Pvalue of 0.102. What probably happens as a result of our testing? Suppose that, in reality,
the machine is producing 99% good parts.
(a) We correctly fail to reject H0.
(b) We correctly reject H0.
(c) We reject H0, making a Type I error.
(d) We fail to reject H0, making a Type I error.
(e) We fail to reject H0, making a Type II error.
4. Which of the following is true about Type I and Type II errors?
I. Type I errors are always worse than Type II errors.
II. Type II errors are always worse than Type I errors.
III. The severity of Type I and Type II errors depends on the situation being tested.
(a) I only
(b) II only
(c) III only
5. Find the P-value for each of the following situations.
(5 points each)
(a) H 0 : p = 0.10, H a : p > 0.10, z* = 2.45
(b) H 0 : p = 0.50, H a : p ¹ 0.50, z* = -1.625
(c) H 0 : m = 82, H a : m < 82, t * = -2.85, n = 8
6. Consider the hypotheses below. Each part of this problem refers to these hypotheses, but
each problem is separate from each other. (5 points each)
H 0 : p = 0.30, H a : p ¹ 0.30
(a) Suppose that in a sample of 350 people, there were 112 “successes”. Calculate
the test statistic for this sample. Show your calculations.
(b) For another sample, the p-value was determined to be 0.0525. What would be the
appropriate conclusion at the  = 0.05 level?
7. Suppose we wanted to construct a 95% confidence interval for the average temperature of
people who contract a new strain of influenza with a margin of error of 0.12. Suppose also
that other studies have supported that the standard deviation of human body temperature is
0.425. How many subjects should be chosen at random for study? (7 points)
8. The calorie content of one half-cup of chocolate ice cream for 5 different brands are as
follows: 150, 170, 140, 160, 160. Construct a 98.5% confidence interval for the true average
number of calories in one half-cup of all brands of chocolate ice cream. Do not forget to
verify that the process is valid. (8 points)
9. The financial aid office at a certain university is concerned about the amount of money
students are spending on textbooks each semester. The director of the office believes that
students are spending, on average, more than $500 each semester. To test this claim, 45
students were randomly selected and the amount spent in the previous semester on textbooks
was recorded. For this group the average was $528 with a standard deviation of $50. Use a
95% confidence interval to test the relevant hypotheses. (10 points)
H0 :
Ha :
95% CI:
Conclusion:
Validity:
10. In 2006, an Associate Press survey was conducted to investigate how people use nutritional
information provided on package labels. Of 1003 respondents, 582 said they do not even
look at the nutritional label. Does this provide evidence that more than half of all Americans
do not look at the nutritional information label when purchasing food? Test the relevant
hypotheses at the  = 0.05 level. (10 points)
H0 :
Validity:
Ha :
Test Stat:
P-value:
Conclusion:
11. A national survey of high school students and high school teachers asked whether the
individual agreed with the statement: “Students should be allowed to report on controversial
issues in their student newspaper without the approval of school authorities.” Of 5000
student responses, 58% said “Y”, and of the 4400 teacher responses, 42% said “Y”. Does
this data support that the proportion of all high school students that would say “Y” is
different than the proportion of all high school teachers that would say “Y”? Use a 95%
confidence interval to test the relevant hypotheses. (10 points)
H0 :
Ha :
95% CI:
Conclusion:
Validity:
12. The question of whether or not taking aspirin reduces the chance of having a heart attack has
been of interest for some time. In one particular experiment, a very large sample was
randomly selected from a pool of people of comparable age and health. One group was
given aspirin every day and the other a placebo. Of the 11034 people that were given a
placebo daily, 189 had a heart attack at some point while only 104 of the 11037 people given
aspirin had a heart attack. Is there significant evidence to support that the proportion of all
people that have a heart attack is lower for those taking aspirin than for those that do not?
Test the relevant hypotheses at the  = 0.05 level. (10 points)
H0 :
Validity:
Ha :
Test Stat:
P-Value =
Conclusion:
13. The Nielsen Company is a global information and media company. Recently, they reported
that U.S. mobile phone subscribers average 3.7 hours per month watching videos on their
phone. Suppose that a random sample of 100 college students in the U.S. was taken, and it
was determined that, in this sample, the average number of hours spent watching videos on
their phone was 6.76 hours with a standard deviation of 3.88 hours. Does this sample
provide evidence that college students are watching videos on their phone more than the
national average? Test the relevant hypotheses at the  = 0.05 level. (10 points)
H0 :
Validity:
Ha :
Test Stat:
P-Value =
Conclusion: