Question 1

Sampling without replacement means that once a member of a population is chosen for a sample, it cannot be chosen again for the same sample.

Accepted Answer

In sampling without replacement, each selected member is removed from the population for the remainder of the sampling process, ensuring it is not selected more than once.

Question 2

With systematic sampling, there is the risk that the person selecting the next member for the sample from the population may be biased in his or her choice.

Accepted Answer

In systematic sampling, the selection of sample members is based on a fixed, periodic interval (e.g., every 10th member from a list), which reduces the risk of personal bias in the selection process.

Question 3

The sampling distribution of the proportion describes the pattern that sample proportions tend to take on when randomly drawn from a population.

Accepted Answer

The sampling distribution of the proportion indeed describes how the sample proportions vary around the true population proportion when samples are randomly drawn from the population.

Question 4

When the proportion of sample size to population size, n/N, is greater than 5%, the finite population correction factor is used to adjust the standard error of the proportion.

Accepted Answer

The finite population correction factor is used to adjust the standard error of the proportion when the sample size is a significant fraction (greater than 5%) of the total population, to account for the reduced variability in samples from finite populations.

Question 5

Suppose the average amount spent per shopper at the Super Fresh Grocery Store last month was
$46.10. A sample of 25 transactions from last month was randomly selected. Another random sample of 50 transactions was also collected. We can be certain that the sampling error from the sample of 50 customers will be less than the sampling error from the 25 customers.

Accepted Answer

Sampling error decreases as sample size increases, but we cannot be certain without knowing the variability of the population and assuming the samples are representative.

Question 6

Excel's random sampling tool uses sampling with replacement.

Accepted Answer

Excel's random sampling tool can perform sampling with replacement, meaning each item can be selected more than once.

Question 7

The average age of the MBA students in a particular statistics class is 30.7 years old. The ages of five randomly selected students from this class are: 36, 25, 25, 29, and 30. The sampling error for this sample is - 1.7 years.

Accepted Answer

Sampling error is the difference between the sample statistic and the population parameter. Here, the average age of the sample (29 years) is 1.7 years less than the population mean (30.7 years), hence a sampling error of -1.7 years.

Question 8

The standard error of the mean is the sample mean standard deviation, which measures the variation around the mean of the sample means.

Accepted Answer

The standard error of the mean measures how much the sample means you would expect to vary from the true population mean. It is indeed related to the standard deviation of the sample means, indicating the precision with which the sample mean estimates the population mean.

Question 9

Sampling error is the difference between a sample statistic and a population parameter.

Accepted Answer

Sampling error occurs because a sample is only a part of the population, and the statistics calculated from the sample may not exactly match the corresponding parameters of the entire population.

Question 10

The bootstrap method can be applied to estimate parameters such as the population proportion, mean, median, or variance.

Accepted Answer

The bootstrap method is a resampling technique used to estimate statistics on a population by sampling a dataset with replacement. It can be applied to estimate various parameters, including the population proportion, mean, median, or variance, by generating numerous samples and calculating the desired statistic for each sample.

Question 11

The higher the standard error of the mean, the less variation you will notice from one sample mean to the next as they are drawn from the population.

Accepted Answer

The higher the standard error of the mean, the more variation you will notice from one sample mean to the next, indicating less precision in estimating the population mean.

Question 12

Measuring the entire population is usually preferred over measuring a sample from the population.

Accepted Answer

Measuring the entire population is often impractical due to time, cost, and logistical constraints, making sampling a more feasible and commonly used method for gathering data.

Question 13

To use the Central Limit Theorem, we need to know the mean and standard deviation of the population.

Accepted Answer

The Central Limit Theorem applies regardless of the population's mean and standard deviation; it states that the sampling distribution of the sample mean will approach a normal distribution as the sample size increases, even if the population distribution is not normal.

Question 14

As the sample size increases, the interval that contains 95% of the sample means becomes narrower.

Accepted Answer

As the sample size increases, the standard error of the mean decreases, leading to a narrower 95% confidence interval for the sample means. This is because larger sample sizes provide a more precise estimate of the population mean.

Quiz 7: Alcohol and Tobacco