Chapter 7 MC

Following a recent dramatic drop of 500 points in the Dow Jones Industrial Average, 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.

Suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. Your sample has a mean of 115 and a standard deviation of 13.8. Which of the following has a mean of 120 and a standard deviation of 3?

• the distribution of the population

• the distribution of the sample data

• the sampling distribution of the sample mean.

• the sampling distribution of the population mean.

• No important distribution related to this situation has the given mean and standard deviation.

• I only

• II only

• III only

• III and either I or II

• All three conditions must be met

The central limit theorem refers to which of the following characteristic 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 $\frac{\sigma}{\sqrt{n}}$

• 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 simple random sample of 1000 Americans found that 62% were satisfied with the service provided by the dealer from which they bought their car. A simple random sample of 1000 Canadians found that 59% were satisfied with the service provided by the dealer from which they bought their car. The sampling variability associated with these statistics i

• exactly the same.

• not exactly the same, but very close.

• much smaller for the sample of Canadians because the population of Canada is much smaller than that of the United States, hence the sample is a larger proportion of the population.

• smaller for the sample of Canadians because the percent satisfied was smaller than that for the Americans.

• larger for the Canadians because Canadian citizens are more widely dispersed throughout the country than are citizens in the United States, hence they have more variable views.

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

• $\mu=45,\ \sigma\$ unknown; shape of distribution unknown

• $\mu=45,\ \sigma=15$ distribution approximately Normal

• $\mu=45,\ \sigma=15$ shape of distribution unknown

• $\mu=45,\ \sigma=3.75$ distribution approximately Normal

• $\mu=45,\ \sigma=3.75$ 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?

• A

• B

• C

• D

• E

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?

• A

• B

• C

• D

• E