Homework 3 (25 points)
STAT 301
Name(s) _____SOLUTION________
Due: Thursday, February 7th @ 11:59pm
1. A study was designed to determine whether dogs can be trained to identify urine specimens
from individuals with bladder cancer. Dogs were first trained to discriminate urine specimens
from patients with bladder cancer or with other conditions. After training was completed, the
dogs had to pick one of seven new urine specimens. Each time, only one of the seven urine
specimens came from a patient with bladder cancer. Out of the 54 trials, the dogs identified the
correct urine specimen 16 times.
Research Question – Is there evidence that trained dogs can correctly identify the urine
specimen from patients with bladder cancer?
a. Identify the population of interest. (1 point)
Population – All dogs
b. Identify the sample. (1 point)
Sample – dogs trained to identify urine specimens
c. Identify the single categorical variable of interest. (1 point)
Identification Status
d. Identify the parameter of interest. (1 point)
p = true proportion of dogs trained that can correctly identify urine specimens
from patients with bladder cancer
e. Identify the statistic. (1 point)
pˆ =
f.
16
= 0.30
54
Determine the appropriate null and alternative hypotheses that would be used to test
the research question of interest. (3 points)
H0: p ≤ 0.14
Ha: p > 0.14
g. Using Tinkerplots®, carry out a simulation study using 1,000 simulated trials. Paste or
provide a detailed sketch of your plot below. (4 points)
Answers will vary, but your spinner should look like the one below.
1
h. Using the plot created in part g, calculate the estimated p-value for this study. (2 points)
To calculate the p-value you want
i.
# of dots at 16 or more
1000
Using the p-value computed in part h, what conclusion can be made regarding the
research question? (3 points)
If the p-value is less than 0.05 then there is evidence that the dogs can
correctly identify urine samples with bladder cancer.
If the p-value is greater than 0.05 then there is not evidence that dogs can
correctly identify urine samples with bladder cancer.
2. For each of the following scenarios, describe in context how the binomial distribution can be
used to model the scenario. (4 points each)
a. Antibiotic resistance occurs when disease-causing microbes become resistant to
antibiotic drug therapy. Because this resistance is typically genetic and transferred to
the next generations of microbes, it is a very serious public health problem. According
to the CDC, 7% of gonorrhea cases tested in 2004 were resistant to the antibiotic
ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 10 cases of
gonorrhea during one week of 2004.
n = 10 cases
2 outcomes: resistant, not resistant
P(resistant) = 0.07 for each case
Cases are independent of one another
b. The actual rate of unintended pregnancies for women taking the pill is 5%. That is, if a
doctor prescribes the pill to 100 new female users, 5 of them will have become pregnant
within one year while taking the pill. A doctor prescribes the pill to 20 new female users
and tracks their pregnancy status within the first year of use.
n = 20 females
2 outcomes: unintended pregnancy, no unintended pregnancy
P(unintended pregnancy) = 0.05 for each female
Females are independent of one another
2