STAT412
Homework 4
Due Friday, Feb. 26
Instructions: If you are asked to carry out a hypothesis test, use traditional and p-value approach to hypothesis testing. Make sure
you show all of the steps! Minitab can be used for this assignment.
1. Twenty volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. Ten of the volunteers
were randomly selected to receive tablets containing 1 gram of vitamin C. These tablets were taken four times a day. The control
group, consisting of the other 10 volunteers, was given placebo tablets that looked and tasted exactly like the vitamin C ones. This was
continued for each volunteer until a doctor, who did not know whether one volunteer was receiving vitamin C or the placebo, decided
that the volunteer was no longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the
experiment, the following data resulted:
Treated With Vitamin C
5.5
6.0
7.0
6.0
7.5
7.5
5.5
7.0
6.5
6.0
Treated With Placebo
6.5
6.0
8.5
7.0
6.5
7.5
6.5
7.5
6.0
8.0
Is there sufficient evidence to conclude that the mean time for patients treated with vitamin C is less than the mean time for the
patients treated with placebo? Use =.05.
2. Twenty-two children, ages 5 to 7 and who liked candy, were matched into 11 pairs based on age, sex, and scores on form L of the
Stanford-Binet intelligence test. Within each pair of children, one student was randomly chosen to receive the experimental treatment
and the other child to receive the control treatment. Seven weeks later, all 22 children were given form M of the Stanford Binet by the
same school psychologist. The control group took the test according to the standard protocol. The experimental group took the test
according to the standard protocol with the exception that the child was promised and given an M & M candy for each correct
response. The results are summarized below.
Experimental
Control
Difference
N
11
11
11
Mean
94.55
83.09
11.45
StDev
14.29
9.25
9.02
Do the data provide sufficient evidence to conclude that the M & M treatment results in higher scores on form M, on average, than the
control protocol? Using the relevant output above, conduct hypothesis test using α = .01 .
3. A wine manufacturer sells a Cabernet with a label that asserts an alcohol content of 11%. Sixteen bottles of this Cabernet are
randomly selected and analyzed for alcohol content. The resulting observations are
10.8
10.2
9.6
9.8
9.5
10.4
11.4
11.1
9.8
10.3
9.1
9.8
10.4
9.0
10.7
9.8
Construct a 95% confidence interval for , the average alcohol content of the bottles of Cabernet produced by this manufacturer.
Interpret the interval!
4. Rolls of paper are acceptable for making bags for grocery stores if the mean breaking strength is more than 40 psi. A manufacturer
has proposed a process to manufacture grocery bags from recycled paper. A test of 25 paper samples from the proposed process has a
mean breaking strength of 40.93 psi and a standard deviation of 2.25 psi. Is there sufficient evidence to conclude the new process is
suitable for manufacturing grocery bags. Use =.05.
5. A safety officer wants to demonstrate that  = the average speed of cars driven by a school is less than 25 mph. Suppose that a
random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Conduct hypothesis test
using =.01.
6. A simple random sample of students is selected, and the students are asked how much time they spent preparing for a test. The
times (in hours) are as follows:
1.3
7.2
4.2
12.5
6.6
2.5
5.5
Based on these results, a confidence interval for the population mean is found to be 5.69  2.70 . Find the degree of confidence.
7. In a test of the effectiveness of a device that is supposed to increase gasoline mileage in automobiles, 12 cars were run over a
prescribed course both with and without the device. The mileages are given below. Conduct hypothesis test at =.05.
Car
1
2
3
4
5
6
7
8
9
10
11
12
Without Device
21
30
29.8
27.3
27.7
33.1
18.8
26.2
28
18.9
29.3
21
With Device
20.6
29.9
30.7
26.5
26.7
32.8
21.7
28.2
28.9
19.9
32.4
22
8. The interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called
Empathetic Concern, measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges
from 0 (less empathetic) to 28 (more empathetic). The following data, representing random samples of 16 males and 16 females, are
consistent with results reported in psychological studies. Can you conclude that there is a difference in mean empathy score between
men and women? Use =.05.
Males
13
20
12
16
13
26
21
23
8
15
18
25
15
23
17
22
Females
22
20
26
25
28
24
16
19
20
23
21
23
15
26
19
25