Sample to Sample Variability

A polling company is considering three sampling procedures over a specific population. Which of the following would have greatest variability?

• 80 samples of size 20

• 50 samples of size 50

• 20 samples of size 80

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the shape, mean and standard deviation of the distribution of sample means from samples of size n = 81.

• Normal,  $\mu_x$  = 4000,  $\sigma_x$  = 1.543

• Normal,  $\mu_x$  = 4000,  $\sigma_x$  = 13.89

• Normal,  $\mu_x$  = 444,  $\sigma_x$  = 13.89

When x̅ differs from sample to sample, we say this is an example of

• variability among the samples

• bias among the samples

• not having large enough sample sizes

• poor survey techniques

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 is

• exactly the same

• not exactly the same, but very close

• much smaller for the sample of Canadians because the population of Canad 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 of Americans.

Taking a larger sample will reduce variability.

• True

• False

If we collected many different sample groups from the same population, we would expect each sample to give slightly different estimates for the population parameter due to the natural differences between the samples. This is known as:

• Simpson's Paradox

• Response bias

• Stratification

• Sampling variability

Select the correct answer: If we take many simple random samples from the same population we expect:

• the same values of the statistic for each sample

• the values of the statistic will vary from sample to sample

• a different value of the parameter for each sample

• a problem with voluntary response

• a problem with bias

Researchers will conduct a study of the television-viewing habits of children. They will select a random sample of children and record the number of hours of television the children watch per week. Which of the following statements is correct?

• A sample of size 25 will produce more variability in the sampling distribution than a sample of size 50 will.

• A sample of size 25 will produce less variability in the sampling distribution than a sample of size 50 will.

• A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

• A sample of size 25 will produce a more normal curve than a sample of size 50 will.

• A sample of size 25 will produce a less biased estimator than a sample of size 50.

Researchers found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season. If samples of 48 high school football players are randomly selected, what is the shape, mean and standard deviation of the distribution of sample means?

• Normal, $\mu_x$ = 355 , $\sigma_x$ = 11.547

• Approximately Normal, $\mu_x$ = 355 , $\sigma_x$ = 80

• Normal, $\mu_x$ = 355 , $\sigma_x$ = 80