Q1. Sampling error can be defined as:

A)   the standard deviation of a sampling distribution of the sample means.

B)   rejecting the null hypothesis when it is true.

C)   the difference between a sample statistic and its corresponding population parameter.

Q2. The sampling distribution of a statistic is:

A)     always a standard normal distribution.

B)     the same as the probability distribution of the underlying population.

C)     the probability distribution consisting of all possible sample statistics computed from samples of the same size drawn from the same population.

Q3. A sample of five numbers drawn from a population is (5, 2, 4, 5, 4). Which of the following statements concerning this sample is most accurate?

A)   The mean of the sample is ∑X / (n − 1) = 5.

B)   The variance of the sample is: ∑(x₁ − mean of the sample)² / (n − 1) = 1.5.

C)   The sampling error of the sample is equal to the standard error of the sample.

Q4. An analyst wants to generate a simple random sample of 500 stocks from all 10,000 stocks traded on the New York Stock Exchange, the American Stock Exchange, and NASDAQ. Which of the following methods is least likely to generate a random sample?

A)    Assigning each stock a unique number and generating a number using a random number generator. Then selecting the stock with that number for the sample and repeating until there are 500 stocks in the sample.

B)    Using the 500 stocks in the S& 500.

C)    Listing all the stocks traded on all three exchanges in alphabetical order and selecting every 20th stock.

Q5. A simple random sample is a sample constructed so that:

A)     the sample size is random.

B)     each element of the population has the same probability of being selected as part of the sample.

C)     each element of the population is also an element of the sample.

答案和详解如下：

Q1. Sampling error can be defined as:

A)   the standard deviation of a sampling distribution of the sample means.

B)   rejecting the null hypothesis when it is true.

C)   the difference between a sample statistic and its corresponding population parameter.

Correct answer is C)

This is the definition.

Q2. The sampling distribution of a statistic is:

A)     always a standard normal distribution.

B)     the same as the probability distribution of the underlying population.

C)     the probability distribution consisting of all possible sample statistics computed from samples of the same size drawn from the same population.

Correct answer is C)

A sample statistic itself is a random variable, so it also has a probability distribution. For example, suppose we start with a sample of the prices of 200 stocks, and we calculate the sample mean of a random sample of 40 of those stocks. If we repeat this many times, we will have many different estimates of the sample mean. The distribution of these estimates of the mean is the sampling distribution of the mean. A statistic’s sampling distribution is not necessarily normal or the same as that of the population.

Q3. A sample of five numbers drawn from a population is (5, 2, 4, 5, 4). Which of the following statements concerning this sample is most accurate?

A)   The mean of the sample is ∑X / (n − 1) = 5.

B)   The variance of the sample is: ∑(x₁ − mean of the sample)² / (n − 1) = 1.5.

C)   The sampling error of the sample is equal to the standard error of the sample.

Correct answer is B)

The mean of the sample is ∑X / n = 20 / 5 = 4. The sampling error of the sample is the difference between a sample statistic and its corresponding population parameter.

Q4. An analyst wants to generate a simple random sample of 500 stocks from all 10,000 stocks traded on the New York Stock Exchange, the American Stock Exchange, and NASDAQ. Which of the following methods is least likely to generate a random sample?

A)    Assigning each stock a unique number and generating a number using a random number generator. Then selecting the stock with that number for the sample and repeating until there are 500 stocks in the sample.

B)    Using the 500 stocks in the S& 500.

C)    Listing all the stocks traded on all three exchanges in alphabetical order and selecting every 20th stock.

Correct answer is B)

The S& 500 is not a random sample of all stocks traded in the U.S. because it represents the 500 largest stocks. The other two choices are legitimate methods of selecting a simple random sample.

Q5. A simple random sample is a sample constructed so that:

A)     the sample size is random.

B)     each element of the population has the same probability of being selected as part of the sample.

C)     each element of the population is also an element of the sample.

Correct answer is B)

Simple random sampling is a method of selecting a sample in such a way that each item or person in the population being studied has the same (non-zero) likelihood of being included in the sample.

I'll be the one.

Q1. Which of the following statements about the variance of a normally distributed population is least accurate?

A)     The Chi-squared distribution is a symmetric distribution.

B)     The test of whether the population variance equals σ₀² requires the use of a Chi-squared distributed test statistic, [(n ? 1)s²] / σ₀².

C)     A test of whether the variance of a normally distributed population is equal to some value σ₀², the hypotheses are: H₀: σ² = σ₀², versus H_a: σ² ≠ σ₀².

Correct answer is A)

The Chi-squared distribution is not symmetrical, which means that the critical values will not be numerically equidistant from the center of the distribution, though the probability on either side of the critical values will be equal (that is, if there is a 5% level of significance and a two-sided test, 2.5% will lie outside each of the two critical values).

Q2. A test of the population variance is equal to a hypothesized value requires the use of a test statistic that is:

A)     F-distributed.

B)     Chi-squared distributed.

C)     t-distributed.

Correct answer is B)

In tests of whether the variance of a population equals a particular value, the chi-squared test statistic is appropriate.

Q3. A munitions manufacturer claims that the standard deviation of the powder packed in its shotgun shells is 0.1% of the stated nominal amount of powder. A sport clay association has reviewed a sample of 51 shotgun shells and found a standard deviation of 0.12%. What is the Chi-squared value, and what are the critical values at a 95% confidence level, respectively?

A)   72; 32.357 and 71.420.

B)   72; 34.764 and 67.505.

C)   70; 34.764 and 79.490.

Correct answer is A)

To compare standard deviations we use a Chi-square statistic. X2 = (n – 1)s2 / σ02 = 50(0.0144) / 0.01 = 72. With 50 df, the critical values at the 95% confidence level are 32.357 and 71.420. Since the Chi-squared value is outside this range, we can reject the hypothesis that the standard deviations are the same.

daan

张萱妍