Exam 19: The Diversity of Samples From the Same Population

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have a mean that is __________ the true population proportion.

For Questions , use the following narrative Narrative: Politics Suppose a population contains 60% Republicans and 40% Democrats. -{Politics narrative} Suppose you take a random sample of 10 people from this population.Are you certain that you would get 6 Republicans and 4 Democrats in your sample? Explain your answer.

Explain, in words that a non-statistics student would understand, why the standard deviation of the various sample means taken from a population is smaller than the standard deviation of the individuals in the population? (In the first situation, assume all samples are of the same size, and that size is large.)

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from means from the various samples will have what approximate shape?

For Questions , use the following narrative Narrative: cell phone owners Suppose numerous random samples of size 2,500 are taken from a population made up of 20% cell phone owners. -{Cell phone owners narrative} What is the chance that less than 20.8% of the people in a sample of size 2,500 from this population will own a cell phone?

Larger samples tend to result in __________ accurate estimates of population values than do smaller samples.

Suppose a certain population was reported in the news as being 60% Republican.You take a random sample of 100 people from this population and find that 67% of your sample is Republican.What can you conclude about the news report, based on your sample results?

{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.The proportions of Republicans from the various samples of size 1,000 will have what approximate standard deviation?

Suppose you do not know anything about what the true population mean is, and you want to estimate it using a sample mean.Which statistical technique would you use, a confidence interval or a hypothesis test?

For Questions , use the following narrative Narrative: Test scores Suppose that test scores on a particular exam have a mean of 77 and standard deviation of 5, and that they have a bell-shaped curve. -{Test scores narrative} Suppose that the test scores are not bell-shaped, but are skewed to the right.You want to take a random sample and estimate the average test scored for this population.You want to be able to use the rule of sample means to interpret your results in this case.Under what (if any) conditions is this possible?

For Questions , use the following narrative Narrative: Politics Suppose a population contains 60% Republicans and 40% Democrats. -{Politics narrative} Suppose numerous random samples of size 1,000 are taken from this population.How will the shape, mean, and standard deviation of the frequency curve for the proportions of Democrats in the samples differ from the shape, mean, and standard deviation of the frequency curve for the proportions of Republicans in the samples?

For Questions , use the following narrative Narrative: cell phone owners Suppose numerous random samples of size 2,500 are taken from a population made up of 20% cell phone owners. -{Cell phone owners narrative} The frequency curve made from proportions of cell phone owners from the various samples of size 2,500 from this population will have what approximate mean and standard deviation?

The standard deviation of the proportions from numerous random samples of size 1,000 from a population will be __________ the standard deviation of the proportions from numerous random samples of size 10,000 from the same population.

For Questions , use the following narrative Narrative: cell phone owners Suppose numerous random samples of size 2,500 are taken from a population made up of 20% cell phone owners. -{Cell phone owners narrative} The chance of having at least 20% cell phone owners in a random sample from this population is 50%, no matter what size the sample is (as long as it is large enough for the Rule for Sample Proportions to apply).Why?

In which of the following situations does the rule for sample proportions apply?

For Questions , use the following narrative Narrative: cell phone owners Suppose numerous random samples of size 2,500 are taken from a population made up of 20% cell phone owners. -{Cell phone owners narrative} Suppose you took a random sample of size 2,500 from this population and found that 21.6% of the people in this sample owned a cell phone.Is this considered to be a reasonable value given the size of this sample? Use the standardized score in your answer.

If numerous large random samples or repetitions of the same size are taken from a population, the proportions from the various samples will have what approximate mean?

A __________ provides a range of possible values for the correct value in a population, whether that correct value is a mean, a proportion, or something else.

In which of the following situations does the rule for sample means not apply?

For Questions , use the following narrative Narrative: cell phone owners Suppose numerous random samples of size 2,500 are taken from a population made up of 20% cell phone owners. -{Cell phone owners narrative} Suppose you took a random sample of size 2,500 from this population and found that 17.6% of them owned a cell phone.Is this considered to be a reasonable value given the size of this sample? Use the standardized score in your answer.