# BUEC 232 Final 40 Multiple Choice Questions Exam

uestion

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: ? = 500 Ha: ? 500

at level ? = 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 is ? = 100, he finds the 95% confidence interval is

502 ? 31. He may conclude

a. H0 cannot be rejected at level ? = 0.05 because 500 is within confidence

interval.

b. H0 cannot be rejected at level ? = 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 estimate ? = 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

significant.

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: ? > 5, HA: ? = 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

violated?

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

c. 0.025

35.A student believes that 20% of all students think pepperoni is their favorite pizza.

He performs a test of hypothesis, H0: p = 0.2, having taken a sample of 200

students and finding that 52 think pepperoni is their favorite. He finds a p-value

of 0.0338, so rejects the null at ? = 0.05. He then computes a 95% confidence

interval for the true proportion and finds it is (0.199, 0.321). He is confused.

20% is in the interval! What is the difference?

a. He made a mistake in one of his calculations.

b. The two use different values of p in computing the standard deviation.

c. He should have used the plus four confidence interval.

36.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. We want to know if

his support has decreased. The test statistic is

a. z = 1.56

b. z = -2.57

c. z = -1.55

37. I want to know which of two manufacturing methods will be better. I create 10

prototypes using the first process, and 10 using the second. There were 3

defectives in the first batch and 5 in the second. Find a 95% confidence interval

for the difference in the proportion of defectives.

a. (-0.62, 0.22)

b. (-0.56, 0.22)

c. (-0.493, 0.160)

38.A sample of 75 students found that 55 of them had cell phones. The margin of

error for a 95% confidence interval estimate for the proportion of all students

with cell phones is

a. 0.084

b. (0.633, 0.833)

c. 0.100

39.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. We want to know if

his support has decreased. In computing a test of hypothesis with ,

what is the estimate of the overall proportion, ?

a. 52%

b. 52.5%

c. 51.5%

40. 100 rats whose mothers were exposed to high levels of tobacco smoke during

pregnancy were put through a simple maze. The maze required the rats to make

a choice between going left or going right at the outset. 80 of the rats went right

when running the maze for the first time. Assume that the 100 rats can be

considered an SRS from the population of all rats born to mothers exposed to

high levels of tobacco smoke during pregnancy (note that this assumption may

or may not be reasonable, but researchers often assume lab rats are

representative of large populations since they are often bred to have uniform

characteristics). Let p be the proportion of rats in this population that would go

right when running the maze for the first time. A 90% confidence interval for p

is

a. 0.8 ± .040.

b. 0.8 ± .066.

c. 0.8 ± .078.