Prob Stat Midterm Review

Prob Stat Midterm review Name:

Standard 1 - Variables

· Identify observational units (cases) and variables, and distinguish types of variables as categorical or quantitative

On July 15, 2004, the Harris Poll released the results of a study asking whether people favored or opposed abolishing the penny. Of a national sample of 2136 adults, 59% opposed abolishing the penny.

1. Which of the following is a categorical variable in the Harris Poll?

(a) the 2004 participants

(b) whether each person favors or opposes abolishing the penny.

(d) the percent of people who oppose abolishing the penny

2. What are the observational units in the study?

(a) the number of people who would abolish the penny in the entire population

(b) the number of people who would abolish the penny in the sample

(d) the percent of people who oppose abolishing the penny

3. Suppose that the observational units in a study are Pennsylvania high schools. Which of the following is not a valid variable?

(a.) whether or not the school has an animal for its mascot

(b.) proportion of students scoring proficient or better on the PSSA at each school

(c.) total number of students at each school

(d.) number of high schools in Pennsylvania which have indoor pools

Standard 2 - Sampling

· Distinguish between populations and samples and between parameters and statistics

4. Suppose that 80% of all American students send a card to their mother on Mother's Day and that you selected a simple random sample of 400 American college students and to determine the proportion of them who send a card to their mother on Mother's Day. Suppose further that in the random sample of 400 students, 300 or 75% of them send a card to their mothers.

(a.) 80% is a parameter, 75% is a statistic.

(b.) 75% is a parameter, 80% is a statistic.

(c.) Both 75% and 80% represent statistics.

(d.) Both 75% and 80% represent parameters.

5. A sample is:

(a.) a number resulting from the manipulation of raw data according to specified rules.

(b.) a subset of a population.

(c.) a characteristic of a population which is measurable.

(d.) a complete set of individuals, objects, or measurements having some common observable characteristic.

For questions 6 and 7 use the following situation:

Suppose that 80% of all American college students send a card to their mother on Mother's Day and that you selected a simple random sample of 400 American college students and to determine the proportion of them who send a card to their mother on Mother's Day. Suppose further that in the random sample of 400 students, 300 or 75% of them send a card to their mothers.

6. Which of the following is true?

(a.) the 400 college students are the population

(b.) the sample size is 400

(c.) all college students in the world are the sample

(d.) the sample is the 300 students who send a card

7. Which of the following is the parameter of interest?

(a.) the proportion of American college students who send a card on Mother’s Day

(b.) the proportion of the 400 students in the sample who send a card

(c.) the proportion of all college students in the world who send a card

(d.) the 300 students in the sample who sent a card

8. Suppose we are interested in the average reading achievement test

score of the currently enrolled students in Edison Elementary School.

The tests would be the observational units. The test scores would be ______while the average score of all students in one teacher’s class is ______.

(a.) an observational unit, a sample

(b.) a sample, a parameter

(c.) a variable, a statistics

1. B

(d.) a population, a variable

Standard 3 - SRS

· Carry out a simple random sample

9. Which one of the following would not be an appropriate method to take a random sample of 10 people from a numbered list of 200 names?

(a.) Use a random number table.

(b.) Write the names on slips of papers, mix well, and select 10 slips of paper.

(c.) Pick 5 make and 5 female names without really thinking about it.

(d.) Use a computer to generate 10 random numbers between 1 and 200.

Below is a list of names numbered 1 to 20. Use the random number table to randomly select 5 names from the list by starting at the beginning of the table and taking pairs of digits.

1 / Sofia / 11 / Dara
2 / Eassa / 12 / Jay
3 / Jeffrey / 13 / Nicole
4 / Shakoya / 14 / Francis
5 / John / 15 / Audrey
6 / Rebecca / 16 / Anthoula
7 / William / 17 / Hiep
8 / Johanna / 18 / Sean
9 / Allyson / 19 / Shanira
10 / Brandon / 20 / Alexis

10. What is the second name selected?

(a.) Dara

(b.) Jeffrey

(c.) Jay

(d.) Allyson

11. What is the fifth name selected?

(a.) Dara

(b.) Jeffrey

(c.) Jay

(d.) Allyson

12. We wish to draw a sample of size 5 without replacement from a population 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is:

11362 35692 96237 90842 46843 62719 64049 17823.

Then the households selected are:

(a) households 11 13 36 62 73

(b) households 11 36 23 08 42

(d) households 11 36 23 56 92

Standard 4 - Sampling Errors

· Critique sampling done by others.

· Recognize bias in poor sampling methods and that random sampling is an unbiased method

13. Which best describes a SRS?

(a.) Gives every member of the population an equal chance of being selected.

(b.) Gives every member of the sample an equal chance of being selected.

(c.) Gives every different sample size an equal chance of being selected.

(d.) Gives every different population an equal chance of being selected.

14. A grocer receives a shipment of apples in a large crate. In order to determine the proportion of apples that are bruised in the large crate of apples, she examines a sample of 20 apples taken from the top of the crate and notes that 5% are bruised. He sampling method could be said to be biased because…

(a.) the apples in this crate may have been damaged during shipment

(b.)this crate of apples may not be representative of all such crates

(c.)she only looked at 20 apples, her sample is too small

(d.)the proportion of apples that are bruised in the sample using only top apples is likely to be smaller than the proportion of apples that are bruised in the entire crate.

15. A simple random sample is a good way to get a useful sample because

(a) the sample is always a good representation of the whole population

(b) this method of sampling will result in unbiased estimates

(d) all of the above are true.

(e) none of the above are true.

16. A survey was conducted by visiting the Haverford High School parking lot to estimate the proportion of cars that were red. The spaes were numbered and a random sample of spaces was selected. Which of the following is NOT correct?

(a) If the sampled stall was empty, we can simply choose another stall, at random, to take its place because it is not likely that the stall being vacant is related to a car being red.

(b) The sample would produce an unbiased estimate of the true proportion of red cars

(c) Even though a random sample was taken from cars in the parking lot, the sample may not be representative of the cars parked at Haverford High School because proportions calculated through random samples can be biased

(d) If a another sample of cars was chosen, it is likely that a different proportion of cars that are red would be obtained.

17. A properly conducted random survey selected 1000 Canadians (from a total population of about 30 million) and 1000 Americans (from a total population of about 300 million). Which of the following is FALSE?

(a) Randomization ensures that both samples will result in unbiased estimates of characteristics of their respective populations.

(b) The precision is determined by the ratio of the sample size to the total population size.

(c) A smaller proportion of the American population has been chosen. Therefore, a particular person has a smaller chance of being selected in America than in Canada.

(d) Random digit dialing to select people for the survey by telephone could induce biases in the results if the characteristic of interest for the survey is related to income.

Standard 5 - Studies

· Distinguish between observational studies and experimental studies

· understand the different types of conclusions that can be drawn from each

· Recognize that in an observational study (e.g. a survey), an observation may be best explained by random sampling variability

18. You are concerned that your employees have little saved for retirement. You conduct a survey of your 100,000 employees using a simple random sample of size 47. You find that the mean of the savings of this sample of employees is $40,000 with standard deviation of $3,000.

This is an example of an…

(a) observational study since subjects are randomly assigned to groups

(b) observational study since it is based on taking a sample of a population without intervening

(d) experiment study since it is based on taking a sample of a population without intervening

19. Researchers concerned about the effects of excessive television viewing on students school performance are planning to conduct a study. Which of the following is true?

(a.) This study would be considered an observational study if they assigned one group of students to watch 4 hours of television each day and another group to not watch any television.

(b.) This study would be considered biased if they assigned one group of students to watch 4 hours of television each day and another group to not watch any TV.

(c.)This study would be considered an experiment if they assigned one group of students to watch 4 hours of television each day and another group to not watch any TV.

(d.) This study would be considered an experiment if they took a random sample of students, recorded their grades and the number of hours of television they watched.

20. Suppose that 80% of all American students send a card to their mother on Mother's Day and that you selected a simple random sample of 400 American college students and to determine the proportion of them who send a card to their mother on Mother's Day. Suppose further that in the random sample of 400 students, 300 or 75% of them send a card to their mothers. This is an example of an…

(a) observational study since subjects are randomly assigned to groups

(b) observational study since it is based on taking a sample of a population without intervening

(d) observational study since it is based on taking a sample of a population without intervening

21. A survey is to be undertaken of recent nursing graduates in order to compare the starting salaries of women and men. For each graduate, three variables are to be recorded (among others) sex, starting salary, and area of specialization.

(a) Sex and starting salary are explanatory variables; area of specialization is a response variable

(b) Sex is an explanatory variable; starting salary and area of specialization are response variables.

(c) Sex is an explanatory variable; starting salary is a response variable; area of specialization is a possible confounding variable

(d) Sex is a response variable; starting salary is an explanatory variable; area of specialization is a possible confounding variable

(e) Sex and area of specialization are response variables; starting salary is an explanatory variable.

Standard 6 - Experimental Design

· Understand principles of control including comparison, replication, randomization, blindness, and blocking

· Carry out a well-controlled experiment

22. A study was conducted to see if Smartfood Popcorn makes people smarter. A group of 50 participants in the study were divided into two groups. One group received Smartfood Popcorn before taking a spelling test, and the other took the test without first getting popcorn. The control group in an experiment should be designed to receive:

(a.) the opposite of the experiences afforded the experimental group.

(b.) the experiences afforded the experimental group except for the treatment under examination.

(c.) the experiences afforded the experimental group except for receiving the treatment at random.

(d.) the experiences which constitute an absence of the experiences received by the experimental group.

23. The Smartfood experiment would be said to take into account the principle of blindness if ______, and it could be said to be double-blind if ______.

(a.) the subjects are randomly assigned to either eat Smartfood or not;

those evaluating the subjects are blindfolded

(b.) the subjects are not aware of which treatment group they are in;

those evaluating the subjects are not aware of which treatment group received Smartfood