Econ 221 Midterm 2

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______. a. Becomes larger b. Becomes smaller c. Is closer to normal distribution d. Is closer to the standard deviation

c. Is closer to normal distribution

If X has a normal distribution with u=100 and o=5, then the probability P(90 <= x <= 95) can be expressed in terms of the standard normal random variable Z as__________. a. P(2 <= Z <= 1) b. P(-2 <= Z <= 1) c. P(-2 <= Z < = -1) d. P(-2 <= Z <= -2)

c. P(-2 <= Z <= -1)

Which of the following is not a characteristic of a probability density function f(x)? a. f(x) >= 0 for all values of x b. f(x) is symmetric around the mean c. The area under f(x) over all values of x equals one d. f(x) becomes zero or approaches zero if increase to +infinity or decreases to -infinity

b. f(x) is symmetric around the mean

The cumulative distribution function is denoted and defines as which of the following? a. f(x) and f(x) = P(X <= x) b. f(x) and f(x) = P(X >= x) c. F(x) and F(x) = P(X <= x) d. F(x) and F(x) = P(X >= x)

c. F(X) and F(X) = P(X <= x)

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car. a. 0.0000 b. 0.5000 c. 0.7580 d. 0.2420

a. 0.0000

The height of the probability density function f(x) of the uniform distribution defined on interval [a,b] is _____. a. 1/(b-a) between a and b, and zero otherwise. b. (b-a)/2 between a and b, and zero otherwise. c. (a+b)/2 between a and b, and zero otherwise. d. 1/(b+a) between a and b, and zero otherwise.

a. 1/(b-a) between a and b, and zero otherwise.

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? a. For any sample size n, the sampling distribution of the sample mean is normally distributed b. For a sample size n < 50, the sampling distribution of the sample mean is normally distributed c. For a sample size n < 30, the sampling distribution of the sample mean is normally distributed d. For a sample size n > 30, the sampling distribution of the sample mean is normally distributed.

a. For any sample size n, the sampling distribution of the sample mean is normally distributed

What can be said about the expected value and standard deviation of an exponential distribution? a. The expected value is equal to the standard deviation b. The expected value is equal to the square of the standard deviation c. The expected value is equal to the reciprocal of the standard deviation d. The expected value is equal to the square root of the standard deviation

a. The expected value is equal to the standard deviation

How many parameters are need to fully describe an normal distribution? a. 1 b. 2 c. 3 d. 4

b. 2

Which of the following meets the requirements of a simple random sample? a. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample b. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. c. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age d. A population contains 10 members under the age of 25 and 20 members over the age of 25.The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25

b. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. A population can be divided into 50 city blocks. the sample will include residents from two randomly chosen city blocks (Cluster) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25 (Stratified)

Which of the following is not a form of bias? a. Potions of the population are excluded from the sample b. Information from the sample is typical of information in the population c. Information from the sample overemphasizes a particular stratum of the population d. Those responding to a survey or poll differ systematically from the norespondents

b. Information from the sample is typical of information in the population

According to the central limit theorem, the distribution of the sample means is normal if ______. a. The underlying population is normal b. The sample size n >= 30 c. The standard deviation of the population is known d. Both the underlying population is normal and the sample size n >=30 are correct

b. The sample size n >= 30

In any production process, variations in the quality of the end product are inevitable. Assignable variation refers to a. The variation caused by stratified random sampling b. The variation caused by the use of the finite correction factor c. Specific events or factors that can usually be identified and eliminated d. A number of randomly occurring events that are part of the production process

c. Specific events or factors that can usually be identified and eliminated

If a 99% confidence interval is constructed instead of 95% confidence interval for the population mean then ________. a. The resulting margin of error will increase and the risk of reporting an incorrect interval will increase b. The resulting margin of error will decrease and the risk of reporting an incorrect interval will increase c. The resulting margin of error will increase and the risk of reporting an incorrect interval will decrease d. The resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

c. The resulting margin of error will increase and the risk of reporting an incorrect interval will decrease

How do the tdf and z distributions differ? a. There is no difference between the two b. The z distribution has broader tails c. The tdf distribution has broader tails d. The z distribution has asymptotic tails, while the tdf distribution does not

c. The tdf distribution has broader tails

What is zα / 2 for a 95% confidence interval of the population mean? a. 0.48 b. 0.49 c. 1.645 d. 1.96

d. 1.96

In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to _______. a. The variation caused by stratified random sampling b. The variation caused by the use of the finite correction factor c. Specific events or factors that can usually be identified and eliminated d. A number of randomly occurring events that are part of the production process

d. A number of randomly occurring events that are part of the production process

Which of the following does not represent a continuous random variable? a. Height of oak trees in a park b. Heights and weights of newborn babies c. Time of flight between Chicago and New York d. The number of customer arrivals to a bank between 10 am and 11 am

d. The number of customer arrivals to a bank between 10 am and 11 am

Bias can occur in sampling. Bias refers to _______. a. The division of the population into overlapping groups b. The creation of strata, which are proportional to the stratum's size c. The use of cluster sampling instead of stratified random sampling d. The tendency of a sample statistic to systematically over - or underestimate a population parameter

d. The tendency of a sample statistic to systematically over - or underestimate a population parameter

Non-response bias occurs when _______. a. The population has been divided into strata b. Portions of the population are excluded from the sample c. cluster sampling is used instead of stratified random sampling d. Those responding to a survey or poll differ systematically from the nonrespondents

d. Those responding to a survey or poll differ systematically from the nonrespondents