In a large city school system with 26 elementaryschools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. Foreach, indicate what kind of sampling strategy is involved and what(if any) biases might result. Assume the schools are homogeneous and differ from each other.

a) Randomlyselect200parentsandsendthemasurvey.Followupwithahome visit iftheydonotreturnthesurveywithinaweek.

Which kind of sampling strategy isinvolved?

A.

This sampling strategy is asimplerandomsample.

B.

This sampling strategy is stratifiedsampling.

C.

This sampling strategy is avoluntaryresponsesample.

D.

This sampling strategy is systematicsampling.

What kind of bias(if any) is most likely toresult?

A.

Response bias could result since the PTA wants parents to agree to this plan.

B.

Undercoveragebiascouldresultsincetheparentsinthesamplemaynotbe representativeofallparents.

C.

UndercoveragebiascouldresultsinceonlyparentsinvolvedwiththePTAwill besampled.

D.

Biascouldresultonlyifthesamplingstrategyisnotfollowedas described.

The managers of a large company wished to know the percentage of employees who feel"extremely satisfied" to work there. The company has roughly 24,000 employees. Three scenarios are given in parts a through c below. For eachscenario, determine the sampling method used by the managers.

a) The managers select a single branch at random and survey every employee of that branch.

A.

The managers used a multistage sample.

B.

The managers used a stratified sample.

C.

The managers used a cluster sample.

D.

The managers used a systematic sample.

E.

The managers used a simple random sample.

b) The managers use the companye-mail directory to contact every 80th employee on the list. Choose the correct sampling method below.

A.

The managers used a multistage sample.

B.

The managers used a cluster sample.

C.

The managers used a stratified sample.

D.

The managers used a simple random sample.

E.

The managers used a systematic sample.

3.

A water dowser claims to be able to sense the presence of water using a forked stick. Suppose we wish to set up an experiment to test her ability. We get 24 identicalcontainers, fill half withwater, and ask the dowser to tell which ones are full and which empty. Complete partsa) throughc) below.

a) How will we randomize thisprocedure?

A.

Arrange the 24 containers in 24 separate locations. Use a random number generator to identify the 12 containers that should be filled with water.

B.

Ask the dowser at different times on different days to identify one container at a time.

C.

Locate the containers in two areas. One area is filled with water and one area is empty.

D.

Fill the first 12 containers with water.

b) The dowser correctly identifies the contents of 14 out of 24 containers. Do you think this level of success is statisticallysignificant?

Yes

No

c) How many correct identifications(out of 24) would the dowser have to make to convinceyou, usingstatistics, that the forked stick trickworks? Assume that statistical significance would mean a success rate of90% or higher.

At least

14

24

22

12

correct identifications.

4.Forty volunteers suffering from insomnia agreed to participate in amonth-long test. Half of the people in each of these groups were randomly assigned to an exerciseprogram, while the others did not exercise. Those who engaged in exercise showed more improvement in their insomnia symptoms. Suppose some of the 40 subjects had maintained a healthyweight, but others were quite overweight. Why might researchers choose to block the subjects by weight level before randomly assigning some of each group to the exerciseprogram?

Select all that apply.

A.

People who are overweight could potentially lose more weight to exercise than those with a healthyweight, and thus are more likely to be thrown off their usual sleep patterns. This additional variability could be mistaken as effectiveness of the treatment.

B.

People who are overweight could be less responsive to exercise. This additional variability could obscure the effectiveness of the treatment.

C.

People who are overweight might have different sleep patterns than those with a healthy weight. This additional variability could obscure the effectiveness of the treatment.

D.

People with a healthy weight are less likely to suffer from insomnia.

5.You want to compare the healthiness and tastiness of blueberries grown with three amounts of a new fertilizer(none, half the recommendedamount, and the full recommendedamount). You allocate 20 blueberrybushes to receive each amount offertilizer, assigning them at random. What is the factor and itslevels? How might the response bemeasured?

What is the factor and itslevels?

A.

The factor is the amount of fertilizer used on each bush. The levels are the different amounts of fertilizer(none, half the recommendedamount, and the full recommendedamount).

B.

The factor is the amount of fertilizer. The levels are the 20 blueberrybushes.

C.

The factor is the type of fruit being tested. The level is the number of bushes that are in the experiment.

D.

The factor is the measured healthiness and tastiness of each blueberry. The level is how each blueberry rates on healthiness and tastiness.

How might the response bemeasured?

A.

You might measure each blueberry by length.

B.

You might measure the healthiness and tastiness of each blueberry on a scale of 1 to 10.

C.

You might measure each blueberry by density.

D.

You might measure each blueberry by weight.