1

Practice Midterm 2

Statistics 10, Professor Lew

1. Suppose from the population of UCLA male undergraduates, a random sample of size 36 is picked and each male's height is measured. Suppose for this random sample, the average height is 69 inches with a standard deviation of 3 inches. What is the 99% confidence interval for the average height of the population?

(a) 67.5 inches to 70.5 inches

(b) 66 inches to 72 inches

(d) 68.5 inches to 69.5 inches

(e) 51 inches to 87 inches

2. The following are the losing scores in ten randomly chosen USC football losses to UCLA (the ten come from all known USC football losses to UCLA):

7, 10, 13, 16, 34, 31, 21, 14, 17, 20

What is the approximate 95% confidence interval estimate of the average USC football loss?

(a) about 18.3 plus or minus (2*.90)

(b) about 18.3 plus or minus (2*2.58)

(d) about 18.3 plus or minus (2*8.17)

(e) about 18.3 plus or minus (2*9.04)

3. A survey research organization asked 1,449 U.S. adults (selected at random) what they considered to be the most serious problem facing America today. 33% said domestic terrorism. Let P denote the proportion of all U.S. adults who think that domestic terrorism is the nation's most serious problem. What is the appropriate standard error for the sample percentage as an estimate of P?

(a) about 0.01%

(b) about 0.47 %

(d) about 18%

(e) about 47%

4. A.C. Nielsen Inc., is an American television rating service. Advertisers wish to know what percentage of households will be watching the UCLA-USC football game on November 21. Fifteen hundred households are surveyed and 100 plan to watch the game on TV. Identify the population, population parameter, and the sample statistic. Assume that all households own a TV set.

(a) U.S. households, percentage of households watching UCLA trounce USC, 6.7% of the households.

(b) UCLA-USC football fans, percentage of households watching UCLA trounce USC, 100 households.

(d) UCLA-USC football fans, percentage of households watching UCLA trounce USC, 6.7% of the households.

(e) Fifteen hundred households, number of households watching UCLA trounce USC, 100 households.

5. Internet surveys have become increasingly popular, here is the latest from CNN's website:

Should the U.S. take military action against Iraq?

Opinion	Percentage	Number of votes
Yes	74%	21,288 votes
No	26%	7,618 votes
	Total	28,906 votes

A recent random-digit-dialing telephone poll of 1,500 U.S. households conducted by a national newspaper showed that less than 50% of the surveyed households answered "Yes" to same question "Should the U.S. take military action against Iraq?"

Which survey do you think better represents the actual opinion of the population of all U.S. households on taking military action against Iraq?

(a) The internet survey is more representative because it is larger

(b) The telephone survey is more representative because it is smaller

(c) The internet survey is more representative because it is does not have non-response bias. Respondents chose to answer the survey voluntarily.

(d) The telephone survey is more representative because the households were selected randomly.

(e) The internet survey is more representative because the respondents were selected randomly.

6. A pumpkin farmer produces pumpkins that average 12lbs in weight, with a standard deviation of two pounds. The pumpkins are packed 16 to a crate. What is the chance that a single crate weighs more than 195 pounds?

(a) Less than 1%

(b) About 7%

(d) About 34%

(e) About 69%

7. Suppose the true percentage of Americans who believe that Elvis Presley is still alive is 15%. We randomly select 100 people and ask if they believe that Elvis Presley is still alive. Calculate the chance that 10 or fewer people will say yes.

(a) less than 1%

(b) about 6%

(d) about 10%

(e) about 44%

8. A fair coin will be tossed some number of times and the object is to guess the total number of heads. There is a $1 penalty for each head that the guess is off. For example, if a coin is tossed 10 times and you guess 5 heads and 4 heads show up, you lose $1. If you guess 5 heads and 6 heads show up, you lose $1.

You have no choice but to play. But you can choose the number of tosses:

(i) 50 tosses

(ii) 100 tosses

Which one should you choose to minimize your losses (i.e. which one is better)?

(a) (i)

(b) (ii)

9. A survey research company switched some years ago to random-digit-dialing. They have a contract to estimate the percentage of people using the internet in several California cities. They are using a sample of size 1,000 in Fresno. It has about 500,000 residents. They get very accurate results for Fresno.

San Diego has about 2 million residents and it is about 4 times the size of Fresno. To get about the same accuracy in San Diego as in Fresno, what should the company do?

(a) They should use a sample size of 16,000 because the accuracy of a percentage depends on the fraction of sample to population in Fresno times 4 (i.e. (1,000/500,000) x 4) multiplied by the population of San Diego.

(b) They should use a sample size of 4,000 because the accuracy of a percentage depends on relative size and San Diego is 4 times the size of Fresno.

(c) They should use a sample size of 2,000 because San Diego is 4 times the size of Fresno and the square root of 4 times 1,000 yields 2,000.

(d) They should use a sample size of 1,000 because accuracy of a percentage depends on sample size, not on relative size.

(e) They should keep the ratio of sample size to population size the same in San Diego as it is in Fresno.

10. An analysis of all pizza delivery times for a well-known national chain reveals the following distribution of delivery times (in minutes):

Time to Delivery	10	15	30	45	60
Percentage of Deliveries	5%	20%	50%	20%	5%

Assume that this distribution never changes and applies to pizza deliveries from this chain now and forever. You and 24 of your best friends order pizza to be delivered in 25 different places around Los Angeles. What is the expected value for the average delivery time?

(a) 12.5 minutes

(b) 22.5 minutes

(d) 30.5 minutes

(e) 32 minutes