Name: __________________________________ Section Number: __________________

Show ALL your work. Solutions with no work where it is necessary will receive NO credit. If you need extra paper raise your hand and ask one of the proctors for some. A normal table is provided at the end of the test. Good Luck.

For questions 1-10 circle the answer which best completes the sentence or answers the question. (3 pts each)

1. A fair coin is tossed one hundred times and the number of heads is recorded. The same coin is then

tossed 1000 times and the number of heads is recorded. We expect,

difference between 500 and the number of heads in the second trial.

(b) to get exactly 500 heads in the second trial.

3. the chance error expressed as a percentage of the number of tosses to be smaller in the first trial than in the second trial.
4. all of the above statements.
1. none of the above statements.

2. A box contains 99 zeros and 1 one. If we make draws from this box with replacement,

1. the probability histogram for the sum of the draws ( when put in standard units) will follow the normal curve after a small number of draws.
2. then the probability histogram for the numbers in the box is close to the normal curve if the number of draws is very large.
3. we can use the binomial formula to compute the chance of getting exactly 3 ones in 10 draws.
4. both (a) and (c) are true.
5. both (a) and (b) are true.

3. When thinking about sample surveys we should remember,

1. a parameter is a numerical fact about a sample, subject to chance variation.
2. the researcher uses the population to compute a statistic.
3. that the parameter may be subject to sampling bias.
4. simple random sampling means drawing the subjects at random without replacement.
5. both (c) and (d).

4. Suppose we were interested in the percentage of A’s given in two different classes, Physics 101

and Psychology 101. So, we conduct a simple random sample of 30 students from each class. The

physics class has 300 students while the Psychology class has 1000 students. We know that,

(a) the accuracy of the estimate of the percentage of A’s in the Physics class is much better than the

2. the correction factor for the standard error of the percentage of A’s is larger for the Psychology class.
3. the expected value for the sample percentage of A’s for the Physics class equals the total number of

(d) you had a better chance of being sampled if you were in the Physics class.

(e) both (b) and (d).

5. If we have a probability histogram for the contents of a box,

1. it should follow the normal curve closely if the number of draws is large.
2. the chance of drawing a particular number from the box is equal to the area of the rectangle above that number on the histogram.
3. we know the number of times a particular number was drawn by the area of the rectangle above that number on the histogram.
4. it is a representation of data we collected.
5. both (a) and (b).

6. We can use the binomial formula to compute,

1. the probability that the top three cards in a well shuffled deck of cards are kings.
2. the probability of getting 5 questions correct out of ten total while guessing on a true/false test.
3. the probability of getting three heads in ten tosses of a coin.
4. both (a) and (c).
5. Both (b) and (c).

7. If the number of draws from a box with replacement is quadrupled ( multiplied by 4) we know,

1. the standard error for the sum of the draws quadruples.
2. the standard deviation of the box doubles.
3. the expected value of the sum of the draws doubles.
4. the histogram of the numbers drawn looks more like the normal curve.
5. none of the above.

8. When the population of interest is extremely large,

1. quota sampling should produce results as reliable as that of a simple random sample.
2. another probability method may be needed since a simple random sample may be difficult to obtain.
3. non-response bias can be ignored.
4. population parameters are subject to more fluctuation.
5. none of the above statements are true.

9. We are interested in the percentage of students at Binghamton University that are democrats. If we

obtain a simple random sample of students,

1. there is a good chance that the sample percentage is equal to the population percentage.
2. we will need to substitute the sample fractions of democrats and non-democrats if we want

3. each student would have an equal chance of being in our study.
1. both (a) and (b) are true.
2. both (b) and (c) are true.

10. When using a statistic to estimate a parameter of a population,

1. the formula estimate = parameter + bias + chance error applies.
2. bias in the sampling technique can be eliminated by taking larger and larger samples.
3. a correction factor is never needed if the sample is a simple random sample.
4. the size of any bias in the process can be estimated by the standard error.

(e) both (a) and (c).

11. Consider the following box:

SD_box= 2.37

We make 144 draws with replacement from this box.

1. ( 3 points) What is the expected value for the sum of the draws?

2. (4 points) What is the standard error for the sum of the draws? (the SD of the box is 2.37)

(c) (7 points) Approximate the chances that the sum of the draws is between 280 and 299 inclusive.

4. (4 points) Draw the new box we need for finding the total number of threes in our sample.

5. (3 points) What is the SD of this new box?

12. Five people are sitting at a bar. They order three draft beers (all the same brand) and two cokes. The

waiter has forgotten who ordered which drinks.

(a) ( 3 points) How many ways can the waiter arrange the drinks in front of the people.

2. ( 3 points) The waiter remembers the first person wanted a coke. How many ways can the drinks be

arranged in front of the people where the first person gets a coke?

13. A box contains 5 blue marbles and 10 red marbles. We draw seven marbles from the box without

replacement.

1. ( 4 points) What is the expected value of the percentage of red marbles in our sample.

2. ( 8 points) Calculate the standard error for the percentage of red marbles in our sample.

14. Two hundred draws are made with replacement from a 0 - 1 box whose contents are unknown to you. Of the two hundred draws, 160 of them are zeros and 40 of them are ones.

1. ( 3 points) What should we use as our estimate of the percentage of ones in the box?

15. You forgot to study for your Biology quiz but have decided to take the quiz anyway. It consists of 25

multiple choice questions and you decide to guess the answers. Each question has five total answers,

only one of which is correct. You earn 1 point for each correct answer.

1. ( 4 points ) Write an expression for the exact probability that you score a 5 on the quiz ( no penalty for

not simplifying.)

2. ( 10 points) Use the normal approximation to estimate your answer in part (a).

16. There are 50,000 households in a certain city. The average number of women in each household is

2.41, with a SD of 1.23. A survey organization plans to take a simple random sample of 400

households, and interview all women living in the sample households.

1. ( 3 points) How many interviews do we expect to have?

2. ( 5 points) About how far off is this estimate?