Exam 19: The Diversity of Samples From the Same Population

Which of the following are examples where you would be interested in estimating the population mean?

For Questions , use the following narrative Narrative: Bananas Suppose a researcher asks the question: What is the average weight of bananas selected for purchase by customers in grocery stores? Assume the distribution of weights is the same across all stores. -{Bananas narrative} How can the researcher go about answering this question? Give a general description of the process.

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 you randomly select a single individual from this population.Where would you expect his/her test score to fall?

In practice you don't know the population value, and you take a sample in order to estimate what the population value is.Once you take a specific sample, is it possible to determine whether or not that sample is an accurate reflection of the population? Explain your answer.

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 you take a single random sample of size 100 from this population, and you get a mean test score of 76.Is this something that you would have expected? Use a probability to justify your answer.

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 range of proportions of cell phone owners is reasonable to expect from this population (assuming your sample size is 2,500)? Justify your answer

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 your sample size was only 250.What range of proportions of cell phone owners is reasonable to expect from this population? Justify your answer

For Questions , use the following narrative Narrative: Bananas Suppose a researcher asks the question: What is the average weight of bananas selected for purchase by customers in grocery stores? Assume the distribution of weights is the same across all stores. -{Bananas narrative} Suppose the researcher takes a sample of 100 shoppers and finds the average weight of their banana purchases to be 2.1 pounds.Can he just go ahead and report that the average banana purchase for all grocery store customers is 2.1 pounds? Why or why not?

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 you take a single random sample of size 100 from this population, and you get a mean test score of 79.Is this something that you would have expected? Use a probability to justify your answer.

Suppose you knew that most samples were likely to provide an answer that is within 10% of the population value.What would also be true in that case?

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 shape?

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

For Questions , use the following narrative Narrative: Politics Suppose a population contains 60% Republicans and 40% Democrats. -{Politics narrative} Is it possible to get a random sample that does not represent the population well, in terms of Democrats and Republicans? Explain your answer.

Samples of size 2,500 will produce estimates of the population value that are __________ times more accurate than samples of size 25.(Assume the population is bell-shaped.Use standard deviation as a measure of accuracy.)

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.Does the rule for sample proportions apply in this situation? Explain your answer.

Name the two basic techniques researchers use to summarize and draw conclusions about a population based on their statistical results from a sample.

When someone reports that their results are found to be 'statistically significant', which type of statistical technique was most likely used?

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} Find and compare the answers to the following two questions; explain why your answers are the same or different.1) One individual is selected at random from the population.What range of test scores is reasonable to expect for this person? 2) A sample of 100 individuals is selected at random from the population.What range of average test scores is reasonable to expect for this group?

Achieving statistical significance is equivalent to __________ the idea that chance alone can explain the observed results.

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 you take numerous random samples of size 100 from this population.Describe the shape and give the mean and standard deviation of the resulting frequency curve.