Math 135 Review Test 2 (Ch. 3, 4, & 5)

Part I – Multiple Choice

1. A statistician employed in a corporation believes that employees who receive better than average increases tend to stay with the company longer. He based his conclusion on reports executed against the employee historical database. This study is an example of

a) anecdotal evidence

b) an observational study based on available data

c) an observational study based on a sample survey

d) an experiment

2. Does drinking coffee help students learn better? A random sample of students at a university is selected and each one is asked whether or not they have performed better on an exam after drinking coffee. This study is an example of

a) anecdotal evidence

b) an observational study based on available data

c) an observational study based on a sample survey

d) an experiment

3. Both my grandmother and my mother have been drinking green tea for years. Both of them exhibit a calm collected demeanor. I begin drinking green tea in the hopes that it will produce a calming effect on my turbulent personality. My decision to start drinking green tea is based on

a) anecdotal evidence

b) an observational study based on available data

c) an observational study based on a sample survey

d) an experiment

4. Does shark fin extract help the symptoms of chronic fatigue syndrome? 12 people who suffer from the syndrome participate in the study. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. The volunteers are checked for symptoms on a regular basis throughout the study. The volunteers do not know if they were given the placebo or the extract and neither does their doctor. This study is an example of

a) a double-blind experiment

b) anecdotal evidence

c) a single-blind experiment

d) an observational study

5. A television station is interested in predicting whether voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phoned in, 1474 (55.98%) were opposed to the increase. The number 55.98% is

a) a statisticc) a sample

b) a parameterd) a population

6. In the previous sample, the type of sample obtained is:

a) a simple random samplec) a stratified sample

b) a voluntary response sampled) a cluster sample

7.The process of taking information from a sample to draw conclusions about a population is called

a) random samplingc) probability

b) statistical inferenced) John Jacob Jingle Heimer Schmidt

8. A group of University of South Florida surgery researchers believe that the drug aprotinin is effective in reducing the blood loss of burn patients who undergo skin replacement surgery. In a clinical trial of 16 burn patients, the patients were first divided into groups (those who were severely burned and those who had moderate or mild burns). Each group was then randomly assigned to receive aprotinin or a placebo and the results were compared. This is an example of

a) An experiment using a completely randomized design

b) An observational study using available information

c) An experiment using multi-stage sampling

d) An experiment using randomized block design

9. Of the survey questions below, circle any that are certain to produce a biased response:

a)Does your business have an e-commerce strategy?

b)Do you think that interest groups should be allowed to give huge sums of money to presidential candidates?

c)Do you support or oppose the proposed tax re-assessment for the city of Troy ?

d)Do you support capital punishment or do you feel that taking a human life is considered cruel and unusual punishment?

10. If a fair die is thrown many times, the proportion of 2’s that are rolled will gradually approach what value?

a) 2/6c) 1/2

b) 1/6 d) none of the above

11. A new assessment survey is to be distributed to faculty. A random sample of departments is selected and everyone in the department is included in the sample. This scenario is an example of which sampling design?

a) stratified samplingc) multi-stage sampling

b) cluster samplingd) systematic sampling

12. A study is conducted to determine whether the average blood pressure for Americans has increased over the past 10 years. A simple random sample (SRS) of 50 people is selected and their average blood pressure is calculated. The average blood pressure for the 50 people is a ______. The true unknown mean blood pressure for all Americans is a ______.

Part II

  1. Can you increase the response rate for a mail survey by contacting the respondents before they receive the survey? A study designed to address this question compared 3 groups of subjects. The first group received a preliminary letter about the survey, the second group was phoned and the third received no preliminary contact. A positive response was defined as returning the survey within 2 weeks. (from James E. Stafford, “Influence of preliminary contact on mail returns”, Journal of Marketing Research).

Response / Intervention
Letter / Phone Call / None
Yes / 171 / 146 / 118
No / 220 / 68 / 455
  1. Identify the explanatory and response variables
  1. Construct appropriate graphs to attempt to determine if there appears to be a relationship between Intervention Type and Response.
  1. Describe the relationship you see from the graphs (if any appears to exist).
  1. Select an SRS of size 5 from a population of 450 people. Use line 131 from the Random Number Table (T4). List the 5 ID’s selected below:
  1. Does massage enable the muscles of tired athletes to recover from exertion faster than usual? To answer this question, researchers recruited 8 amateur boxers and 8 amateur soccer players to participate in an experiment. Researchers wanted to determine if there was a different in how the boxers reacted to how the soccer players reacted? After a 20 minutes workout, each athlete was randomly assigned to receive a massage or not. The heart rate and blood lactate levels were used to measure whether the athlete “recovered” from the exertion.

Outline the design for this experiment (use “sport type” as the blocking variable) and then perform the randomization necessary to put the subjects into groups (starting with line 125 in the table of random digits).

Boxers / Soccer Players
1. Hanson / 1. Clark
2. Henry / 2. Jones
3. Smith / 3. James
4. Carlton / 4. Conner
5. McLean / 5. Davies
6. Hampshire / 6. Moller
7. Maher / 7. Moses
8. Tyson / 8. Jannis
  1. Choose an employee at random from a company and observe their annual salary. The table below shows the probability of each salary category in this company:

Salary (in thousands) / < 25 / 25-49 / 50-75 / >75
Probability / 0.09 / 0.54 / 0.36 / ??

b)Find the ?? probability.

c)Find the probability that the random person selected has a salary that is < $50,000.

d)Let A be the event that a person makes less than $25,000. Describe the event Ac in words and then find the probability of Ac

e)Suppose 2 employees are selected at random. Assuming independence, what is the probability that both employees make less than $25,000? That one employee makes less than $25,000 and one does not? (Assume that order matters).

  1. Suppose in a married couple the probability that the wife smokes is 0.24 and the probability that the husband smokes is 0.32. The probability that both the husband and the wife smoke is 0.18. A married couple is selected at random.
  2. Find the probability that either of them smokes.
  3. Find the probability that neither of them smokes.
  4. What is the probability that the husband does not smoke?
  1. Consider the following probability distribution:

X / −2 / 0 / 1 / 2
Probability of X / 0.03 / 0.25 / 0.4 / 0.32
  1. X is what type of random variable in this example?
  2. Is this a valid probability distribution? How do you know?
  3. Find P(X < 1)
  4. Find P(X ≥ 0)
  1. Let X represent a number that is randomly generated between 0 and 8. X is a continuous random variable.
  2. Draw a picture of the probability distribution of X (the “rectangle”)
  1. Find P(X > 5.2)
  1. Find P(0.3<X<2.6)
  1. A population has a mean of 500 and a standard deviation of 30. Many random samples are selected from the population (all with 36 items).
  2. Find the mean of the sampling distribution for . That is, find .
  1. Find the standard deviation for the sampling distribution for .
  1. What is the shape for the sampling distribution for ? What theorem allows you to draw this conclusion?
  1. WageWeb provides compensation information and services on more than 160 positions. As of October 1, 2003, the national average salary for a registered nurse (RN) was $47,858. Suppose the standard deviation is $7750.
  2. Find the probability that the sample mean for 100 randomly selected nurses is less than $45,000.
  1. Find the probability that the sample mean for 50 selected nurses is greater than $50,000.
  1. According to a CNN report, 7% of the population do not have traditional phones and instead rely only on cell phones. Suppose a random sample of 750 telephone users is obtained.
  2. Describe the sampling distribution for , the sample proportion that are “cell-phone only”.
  3. In a random sample of 750 telephone users, what is the probability that more than 8% are “cell-phone only”?
  4. Would it be unusual if a random sample of 750 adults results in 40 or fewer being “cell-phone only”
  1. Suppose we know that the weight of male runners in the U.S. conform to a Normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. A runner is selected at random.
  2. What is the probability that the runner’s weight is less than 135 pounds?
  1. What is the probability that the runner’s weight is greater than 160 pounds?
  1. What is the probability that the runner’s weight is between 140 and 160 pounds?
  1. Suppose a random sample of 10 runners is selected. What is the probability that the sample mean for the ten runners is less than 135 pounds? Would this be considered an unusual event?

Math 135 Review Test 2

Answer Key

Part I: Multiple Choice

  1. b
  2. c
  3. a
  4. a
  5. a
  6. b
  7. b
  8. d
  9. d
  10. b
  11. b
  12. statistic; parameter

Part II:

1.a) E-Intervention Type R-Response

b) Conditional Distribution of Response given Intervention:

Letter: Y 44% N 56%

Phone Call: Y 68% N 32%

None: Y 21% N 79%

c) In general, intervention via phone call seemed to produce the best response rate

2. ID’s: 050, 071, 281, 194, 148

  1. Will cover in class
  2. b) 0.01c) 0.63d) Person makes at least $25,000; 0.91 e) 0.0081; 0.1638
  3. a) 0.38b) 0.62c) 0.68
  4. a) discreteb) yes; probabilities are all between 0 and 1 (inclusive) and the probabilities sum to 1

c) 0.28

d) 0.97

  1. a) rectangle with length of 8 and a height of 1/8

b) 0.35

c) 0.2875

  1. a) 500b) 30/sqrt(36) = 5c) Normal; Central Limit Theorem
  2. a) z-score “off the chart” on the low side; probability is < 0.0002 which means it is essentially zero (or very close to zero)

b) 0.0256

  1. a) distribution for p-hat is Normal with a mean of 0.07 and a standard deviation of approximately 0.009317

b) 0.1423

c)0.0367

  1. a) 0.1587b) 0.2514c) 0.4972d) 0.0008; highly unusual