105 Math 116 – 03: Test #5 (Chapters 20 – 23)
Name:
Fall 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 – 3 are worth 5 points each.
1. A P-value for a hypothesis test indicates:
(a) the probability of obtaining a sample similar to the one we have assuming that the null
hypothesis is true
(b) the probability of obtaining a sample similar to the one we have assuming that the
alternative hypothesis is true
(c) the probability that the null hypothesis is true
(d) the probability 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 : p̂ = 0.80
H a : p̂ > 0.80
(c)
H 0 : p > 0.80
H a : p = 0.80
(d)
H 0 : m = 0.80
H a : m > 0.80
(e)
H 0 : p = 0.80
H a : p > 0.80
(f)
H 0 : x = 0.80
H a : x > 0.80
3. Suppose we are testing the hypotheses H0:  = 28.4 vs. Ha:  < 28.4 to check whether or not
the machine filling the boxes of cereal labeled 28.4oz is under-filling the boxes. From a
large, randomly selected sample we obtain a P-value of 0.0325. Suppose that in actuality the
machine is not under-filling the boxes. What happens as the result of out testing?
(a) We reject H0, making a type II error.
(b) We fail to reject reject H0, making a type I error.
(c) We reject H0, making a Type I error.
(d) We fail to reject H0, making a Type I error.
4. Find the P-value for each of the following hypothesis tests.
(5 points each)
(a) H 0 : p = 0.15, H a : p < 0.15, z = -2.285
(b) H 0 : p = 0.72, H a : p ¹ 0.72, z = -1.459
(c) H 0 : m =12775, Ha : m >12775, t =1.988, n = 8
5. Consider the hypotheses below. Each part of this problem refers to these hypotheses, but
each part is separate from each other. (5 points each)
H0: p = 0.74, Ha: p ≠ 0.74
(a) Suppose that in a sample of 250 people, there were 192 “successes”. Calculate the
test statistic for this sample. Show your calculations.
(b) For another sample, the P-value is determined to be 0.0685. What would be the
appropriate conclusion at the  = 0.05 level? Why?
(c) For yet another sample, the 95% confidence interval based on this sample turns out to
be ( 0.6845, 0.7285) . What would be the appropriate conclusion? Why?
6. 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 0.08. Suppose also
that other studies have supported that the standard deviation of human body temperature is
0.415. How many subjects should be chosen at random for study? (5 points)
7. Six bags of Doritos are randomly selected for investigation. The weight of each (in grams) is
carefully measured and recorded below. (5 points each)
29.2
28.5
28.7
28.9
29.1
29.5
(a) Show that the sample data is consistent with having come from a normal population.
(b) Use the sample to construct a 96% confidence interval for the true average weight of
Dorito bags of this size.
(c) The Frito-Lay Company labels each of this size bag of chips as containing 28.3 grams.
Comment on whether or not consumers should be concerned about this.
8. In 2006, an Associated 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 using a 95% confidence interval. (10 points)
H0 :
Ha :
95% CI:
Conclusion:
Validity:
9. Among randomly selected teens aged 15-17, 57% of the 248 boys had posted online profiles,
compared to 70% of the 256 girls. Does this sample data support the statement that for teens
ages 15-17, girls are more likely to post online profiles than boys? Test the relevant
hypotheses at the  = 0.05 level. (10 points)
H0 :
Ha :
Test Stat:
P-value:
Conclusion:
Validity:
10. A new process for producing synthetic gems is being tested to see whether or not the true
average weight of gems produced via this process is 0.55 carats. A random sample of 6 gems
was selected, and the weights (in carats) were 0.43, 0.5, 0.46, 0.49, 0.6, 0.55. Test the
relevant hypotheses at the  = 0.10 level. (10 points)
H0 :
Ha :
Test Stat:
P-value:
Conclusion:
Validity:
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: