MSIT Exam 2 Practice Exam Questions
with Complete Answers.
A mattress company would like to claim that sleeping on their state-of-the-art mattresses leads to
greater productivity at work. They select two random samples of workers, half of which will sleep on a
regular mattress and the other half will sleep on their special mattress. The next day, they give all the
employees a difficult task and rate their performance on a scale from 1-100 (higher is better).
(a) Which type of test is described above?
A. one sample z-test
B. two sample t-test
C. t-test for paired data
D. one sample t-test - CORRECT ANSWER B. two sample t-test
Since the company tested two different sample of employees, they are using a test of two independent
means.
A mattress company would like to claim that sleeping on their state-of-the-art mattresses leads to
greater productivity at work. They select two random samples of workers, half of which will sleep on a
regular mattress and the other half will sleep on their special mattress. The next day, they give all the
employees a difficult task and rate their performance on a scale from 1-100 (higher is better).
(b) Would you recommend that the company switch to a paired design, measuring employees
productivity once after sleeping on a regular mattress and once after sleeping on the special mattress (in
randomized order)?
A. Yes, a paired design would likely provide stronger evidence in this context.
B. No, a paired design is not practical in this context. - CORRECT ANSWER A. Yes, a paired design would
likely provide stronger evidence in this context.
, The company would get much stronger evidence their mattresses work by using a paired design. In the
original test of two independent means, it's possible that employees who are naturally more productive
end up in the regular mattress sample and employees who are naturally less productive end up in
special mattress sample, leading to very weak evidence. Seeing how much specific employees improve
their productivity on the special vs. regular mattresses leads to a better measure of how much they help
people be productive.
In some cities, the subway transportation system utilizes the honor system, in which passengers are
requested to buy tickets but are not forced to.
(a) In one city, city officials have subway riders fill out an anonymous survey asking if they've paid for
their ticket. How many riders should they ask if they want to estimate the true proportion who don't buy
tickets within 2%, using 98% confidence?
__________________________ - CORRECT ANSWER 3383
Since no previous estimate of p is available, use p = 0.5. Then n = (z*/ME)^2pq = (2.3263/0.02)2(0.5)(0.5)
= 3382.29 which rounds up to 3383 (sample size always rounds up).
In some cities, the subway transportation system utilizes the honor system, in which passengers are
requested to buy tickets but are not forced to.
(b)(i) In another city, city officials take an anonymous survey of 171 randomly chosen riders of which
20% had not bought a ticket. Construct a 95% confidence interval for the proportion of passengers who
don't buy subway tickets in this city.
___________________________ - CORRECT ANSWER (.1400,.2600)
The confidence interval is given by (sample statistic) ± (critical value)SE. Here, the sample statistic is p̂ =
0.2 and SE = sqrt(0.2*0.) = 0.0306.
The critical value is obtained through the JMP Normal calculator with mean = 0 and SD = 1. Select "Input
probability" and enter Central Probabiity = 0.95, which shows 1.96.
Then the interval is given by 0.2 ± (1.96)(0.0306) = (0.1400, 0.2600).
with Complete Answers.
A mattress company would like to claim that sleeping on their state-of-the-art mattresses leads to
greater productivity at work. They select two random samples of workers, half of which will sleep on a
regular mattress and the other half will sleep on their special mattress. The next day, they give all the
employees a difficult task and rate their performance on a scale from 1-100 (higher is better).
(a) Which type of test is described above?
A. one sample z-test
B. two sample t-test
C. t-test for paired data
D. one sample t-test - CORRECT ANSWER B. two sample t-test
Since the company tested two different sample of employees, they are using a test of two independent
means.
A mattress company would like to claim that sleeping on their state-of-the-art mattresses leads to
greater productivity at work. They select two random samples of workers, half of which will sleep on a
regular mattress and the other half will sleep on their special mattress. The next day, they give all the
employees a difficult task and rate their performance on a scale from 1-100 (higher is better).
(b) Would you recommend that the company switch to a paired design, measuring employees
productivity once after sleeping on a regular mattress and once after sleeping on the special mattress (in
randomized order)?
A. Yes, a paired design would likely provide stronger evidence in this context.
B. No, a paired design is not practical in this context. - CORRECT ANSWER A. Yes, a paired design would
likely provide stronger evidence in this context.
, The company would get much stronger evidence their mattresses work by using a paired design. In the
original test of two independent means, it's possible that employees who are naturally more productive
end up in the regular mattress sample and employees who are naturally less productive end up in
special mattress sample, leading to very weak evidence. Seeing how much specific employees improve
their productivity on the special vs. regular mattresses leads to a better measure of how much they help
people be productive.
In some cities, the subway transportation system utilizes the honor system, in which passengers are
requested to buy tickets but are not forced to.
(a) In one city, city officials have subway riders fill out an anonymous survey asking if they've paid for
their ticket. How many riders should they ask if they want to estimate the true proportion who don't buy
tickets within 2%, using 98% confidence?
__________________________ - CORRECT ANSWER 3383
Since no previous estimate of p is available, use p = 0.5. Then n = (z*/ME)^2pq = (2.3263/0.02)2(0.5)(0.5)
= 3382.29 which rounds up to 3383 (sample size always rounds up).
In some cities, the subway transportation system utilizes the honor system, in which passengers are
requested to buy tickets but are not forced to.
(b)(i) In another city, city officials take an anonymous survey of 171 randomly chosen riders of which
20% had not bought a ticket. Construct a 95% confidence interval for the proportion of passengers who
don't buy subway tickets in this city.
___________________________ - CORRECT ANSWER (.1400,.2600)
The confidence interval is given by (sample statistic) ± (critical value)SE. Here, the sample statistic is p̂ =
0.2 and SE = sqrt(0.2*0.) = 0.0306.
The critical value is obtained through the JMP Normal calculator with mean = 0 and SD = 1. Select "Input
probability" and enter Central Probabiity = 0.95, which shows 1.96.
Then the interval is given by 0.2 ± (1.96)(0.0306) = (0.1400, 0.2600).
