Probability and Sampling

• True

• False

When finding our sample size, if the result is not a whole number, then we round ____.

(Hint: Your answer should be one word.)

Select all that apply. When determining a sample size:

• We need to know E.

• We need to find the t-score.

• We need to find the z-score.

• We need to know the confidence interval.

Consider the following problem:

We wish to do a survey of students at Studymore University to determine a 90% confidence interval for the proportion of students who change their major at least once while enrolled. We need to be within .01 of the true proportion. If no preliminary study is available, how large should we make our sample?

Does this problem involve finding a sample size for a Binomial or a Large Sample? If it is a Binomial do we know p hat or not?

• Binomial, we know p hat.

• Large Sample

• Binomial, we don't know p hat.

Consider the following problem:

Suppose we do a preliminary study for our estimation of p, the proportion of students at Studymore University who change their majors and find that out of 1527 in the study, 1038 changed their majors at least once while at Studymore. How many MORE would we need for our sample in order to be within .01 of the true proportion with a 90% confidence interval?

Does this problem involve finding a sample size for a Binomial or a Large Sample? If it is a Binomial do we know p hat or not?

• Binomial, we know p hat.

• Large Sample

• Binomial, we don't know p hat.

Consider the following problem:

A study on physical attractiveness found a confidence interval for the population mean of a rating which was done on a scale of 1 to 5 where 231 subjects were rated for attractiveness. In the sample, we used the mean was 3.94 and the standard deviation was .75. Suppose we are asked to form a 95% confidence interval so that we are within E = .05 of the population mean. How large should our sample size be?

Does this problem involve finding a sample size for a Binomial or a Large Sample? If it is a Binomial do we know p hat or not?

• Binomial, we know p hat.

• Large Sample

• Binomial, we don't know p hat.

A ponderosa pine forest in Colorado has a pine beetle infestation. The beetles bore into a tree and carry a fungus that ultimately kills the tree. Let p be the proportion of trees in the forest that are infested.

If no preliminary sample is taken to estimate p, how large a sample is necessary to be 85% sure that a point estimate will be within a distance of .06 from p?

A ponderosa pine forest in Colorado has a pine beetle infestation. The beetles bore into a tree and carry a fungus that ultimately kills the tree. Let p be the proportion of trees in the forest that are infested.

A preliminary study of 58 trees showed that 19 were infested. How many trees should be included in the sample to be 85% sure that a point estimate will be within a distance of .06 from p?

George is thinking of buying a sporting goods store in Dove Creek, Montana. However, daily cash flow is an important consideration. A random sample of 40 business days from the past year was taken from the store records. For each day the net income was determined. The sample standard deviation was found to $57.19.

How many business days should be included in the sample to be 85% confident that the sample mean of daily net incomes is within $10 of the population mean of daily net incomes?