Sampling distribution-Chap 7-MC

Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. Which of the following terms describes the number 92%?

• statistic

• sample

• sample parameter

• population parameter

• population

What is distribution of values taken by a statistic in all possible samples of the same size from the same population called?

• the probability that the statistic is obtained

• the population parameter

• the variance of the values

• the sampling distribution of the statistic

• the distribution of sample data

If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?

• random

• biased

• a proportion

• unbiased

• non-varying

The central limit theorem refers to which of the following characteristics of the sampling distribution of the sample mean?

• Regardless of the shape of the population’s distribution, the sampling distribution of the sample mean from sufficiently large samples will be approximately Normally distributed.

• Regardless of the shape of the population’s distribution, the standard deviation of the sampling distribution of the sample mean from sufficiently large samples will be σ/√n.

• Regardless of the shape of the population’s distribution, the mean of the sampling distribution of the sample mean from sufficiently large samples will be equal to the mean of the population.

• As you take larger and larger samples from a Normally distributed population, the standard deviation of the sampling distribution of the sample mean gets smaller and smaller.

• As you take larger and larger samples from a Normally distributed population, the mean of the sampling distribution of the sample mean gets closer and closer to the population mean.

A student investigating study habits asks a simple random sample of 16 students at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are μ = 45 minutes and σ = 15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample?

• μx = 45; σx unknown; shape of distribution unknown

• μx = 45; σx = 15; distribution approximately Normal

• μx = 45; σx = 15; shape of distribution unknown

• μx = 45; σx = 3.75; distribution approximately Normal

• μx = 45; σx = 3.75; shape of distribution unknown

Olive weights are classified according to a unique set of adjectives implying great size. For example, the mean weight of olives classified as "Colossal" is 7.7 gm. Suppose a particular company's crop of "Colossal" olives is approximately Normally distributed with a mean of 7.7 gm and a standard deviation of 0.2 gm. Which of the following represents the probability that the mean weight of a random sample of 3 olives from this population is greater than 8 gm?

• P(z > (8-7.7)/(0.2/√3))

• P(z > (7.7-8)/(0.2/√3))

• P(z < (8-7.7)/(0.2/√3))

• P(z > (8-7.7)/(0.2)(0.8)√3)

• P(z < (8-7.7)/(0.2)(0.8)√3)

In a large population, 46% of the households own DVD recorders. A simple random sample of 100 households from this population is to be contacted and the sample proportion computed. Which of the following expressions represents the probability that more than half the households sampled will own a DVD recorder?

• P(z > (0.46-0.5)/(0.5)(0.5)√100)

• P(z < (0.5-0.46)/(0.5)(0.5)√100)

• P(z > (0.46-0.5)/(0.46)(0.54)√100)

• P(z > (0.46-0.5)/(0.46)(0.54)√100)

• P(z > (0.5-0.46)/(0.46)(0.54)√100)

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x̄, recorded for each sample. Which of the following is the best description of the sampling distribution of x̄?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

Suppose that public opinion in a large city is 65 percent in favor of increasing taxes to support the public school system and 35 percent against such an increase. If a random sample of 500 people from this city are interviewed, what is the approximate probability that more than 200 of these people will be against increasing taxes?

•  binom(500,200) 

  (0.65)²⁰⁰(0.35)³⁰⁰

• binom(500,200)(0.35)²⁰⁰(0.65)³⁰⁰

• P(z > (0.40 - 0.65)/√{(0.65)(0.35)/500}

• P(z > (0.40 - 0.35)/√{(0.4)(0.6)/500}

• P(z > (0.40 - 0.35)/√{(0.35)(0.65)/500}

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881