STATS Multiple Choice Questions Exam

| August 30, 2017

1. Ginger root is used by many as a dietary supplement. A manufacturer of
supplements produces capsules that are advertised to contain at least 500 mg.
of ground ginger root. A consumer advocacy group doubts this claim and tests
the hypotheses
H0:a = 500 Ha:a 500
at levela = 0.05. To do so, he computes that average Math SAT score of all the
students in his class and constructs a 95% confidence interval for the population
mean. The mean Math SAT score of all the students was 502 and, assuming the
standard deviation of the scores isa = 100, he finds the 95% confidence interval is
502± 31. He may conclude
a. H0 cannot be rejected at levela = 0.05 because 500 is within confidence
b. H0 cannot be rejected at levela = 0.05, but this must be determined by
carrying out the hypothesis test rather than using the confidence interval.
c. We can be certain that H0 is not true.
6. I wish to find a 95% confidence interval for the mean number of times men
change channels with a remote control during a commercial. Based on a
preliminary study, I estimates = 15. How many commercials’ worth of data do
I need to have a margin of error no more than 3?
a. 10
b. 97
c. 96
7. Experiments on learning in animals sometimes measure how long a laboratory
rat takes to find its way through a maze. Suppose for one particular maze, the
mean time is known to be 20 seconds with a standard deviation of = 2
seconds. Suppose also that times for laboratory rats are normally distributed. A
researcher decides to test whether rats exposed to cigarette smoke take longer
on average to complete the maze. She exposes 25 rats to cigarette smoke for 15
minutes and then records how long each takes to complete the maze. The mean
time for these rats is 20.6 seconds. Are these results significant at the =
0.05 level? Assume the researcher’s rats can be considered a SRS from the
population of all laboratory rats.
a. Yes.
b. No.
c. The question cannot be answered since the results are not practically
8. The times for untrained rats to run a standard maze has a N (65, 15) distribution
where the times are measured in seconds. The researchers hope to show that
training improves the times. The alternative hypothesis is
a. Ha: µ > 65.
b. Ha: > 65.
c. Ha: µ 5
b. H0:m > 5, HA:m = 5
c. H0: = 5, HA: > 5
28.A bank is investigating ways to entice customers to charge more on their credit
cards. (Banks earn a fee from the merchant on each purchase, and hope to
collect interest from the customers as well). A bank selects a random group of
customers who are told their “cash back” will increase from 1% to 2% for all
charges above a certain dollar amount each month. Of the 500 customers who
were told the increase applied to charges above $1000 each month, the average
increase in spending was $527 with standard deviation $225. Of the 500
customers who were told the increase applied to charges above $2000 each
month, the average increase in spending was $439 with standard deviation
$189. When testing whether or not the increases in spending are different, the
test is significant at
a. 5%
b. 1%
c. 0.5%
29.A researcher wished to compare the average amount of time spent in
extracurricular activities by high school students in a suburban school district
with that in a school district of a large city. The researcher obtained an SRS of 60
high school students in a large suburban school district and found the mean time
spent in extracurricular activities per week to be = 6 hours with a standard
deviation s1 = 3 hours. The researcher also obtained an independent SRS of 40
high school students in a large city school district and found the mean time spent
in extracurricular activities per week to be = 4 hours with a standard
deviation s2 = 2 hours. Let µ 1 and µ 2 represent the mean amount of time spent
in extracurricular activities per week by the populations of all high school
students in the suburban and city school districts, respectively. If the researcher
used the more accurate software approximation to the degrees of freedom, he
would have used which of the following for the number of degrees of freedom for
the two-sample t procedures?
a. 39.
b. 59.
c. 98.
30. We wish to see if the dial temperature for a certain model oven is properly
calibrated. Four ovens of a certain model are selected at random. The dial on
each is set to 300° F and after one hour, the actual temperature of each is
measured. The temperatures measured are 305°, 310°, 300°, and 305°.
Assuming that the actual temperatures for this model when the dial is set to
300° are normally distributed with mean µ , we test whether the oven is properly
calibrated by testing the hypotheses
H 0: µ = 300, H a: µ ? 300.
Based on the data, the P -value for this test is
a. between 0.10 and 0.05.
b. between 0.05 and 0.025.
c. between 0.025 and 0.01.
31.An inspector inspects large truckloads of potatoes to determine the proportion p
with major defects prior to using the potatoes to be made into potato chips. She
intends to compute a 95% confidence interval for p. To do so, she selects an SRS
of 50 potatoes from the over 2000 potatoes on the truck. Suppose that only 2 of
the potatoes sampled are found to have major defects. Which of the following
assumptions for inference about a proportion using a confidence interval are
a. The population is at least 10 times as large as the sample.
b. n is so large that both the count of successes n and the count of failures
n (1 – ) are 10 or more.
c. There appear to be no violations.
32.A manufacturer receives parts from two suppliers. An SRS of 400 parts from
supplier 1 finds 20 defective. An SRS of 100 parts from supplier 2 finds 10
defective. Let p1 and p2 be the proportion of all parts from suppliers 1 and 2,
respectively, that are defective. A 98% confidence interval for p1 – p2, the
difference in the two proportions is
a. -.05± 0.033.
b. -.05± 0.068.
c. – .05± 0.074.
33. I want to estimate the proportion of individuals in my area who think the public
school system needs major overhauling. If I believe the proportion will be about
35%, how many individuals will I need to sample if I want a 95% margin of error
to be no more than 3%?
a. At least 30.
b. At least 1068.
c. At least 972.
34.A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after
the poll is taken, it is disclosed that he had an extramarital affair. A new poll
finds that 50% of the 1030 polled now favor the incumbent. The standard error
for a confidence interval for the candidate’s latest support level is
a. 0.016
b. 0.020

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