A sampling at the mall You have probably seen the mall interviewer, approaching people passing by with a clipboard in hand. Explain why even a large sample of mall shoppers would not provide a trustworthy estimate of the current unemployment rate.
Because the unemployed have more time off than those who reside in the mall, the unemployment rate will most likely be greater.
Given the sample size,
Because the provincial health-care system is meeting its objectives, the Ministry of Health conducted the Ontario Health Survey.
A simple random sample (SRS) of size n is made up of people chosen from the population with an equal chance of being the sample that is actually chosen.
A big sample of mall customers would not produce a reliable estimate of the current unemployment rate because it is easy to find a large number of people in a mall, hence this is a convenience sample. Because the unemployed have more time to spend at the mall than those who are employed, a large sample of mall visitors would not yield a reliable estimate of the present unemployment rate.
Dead trees On the west side of Rocky Mountain National Park, many mature pine trees are dying due to infestation by pine beetles. Scientists would like to
use sampling to estimate the proportion of all pine trees in the area that have been infected.
(a) Explain why it wouldn’t be practical for scientists to obtain an SRS in this setting.
(b) A possible alternative would be to use every pine tree along the park’s main road as a sample. Why is this sampling method biased?
(c) Suppose that a more complicated random sampling plan is carried out, and that of the pine trees in the sample are infested by the pine beetle. Can
scientists conclude that 35% of all the pine trees on the west side of the park are infested? Why or why not?
In an interesting experiment, researchers examined the effect of ultrasound on birth weight. Pregnant women participating in the study were randomly assigned to one of two groups. The first group of women received an ultrasound; the second group did not. When the subjects’ babies were born, their birth weights were recorded. The women who received the ultrasounds had heavier babies.
Did the experimental design take the placebo effect into account? Why is this important?
Sampling gravestones The local genealogical society in Coles County, Illinois, has compiled records on all gravestones in cemeteries in the county from the years to Historians plan to use these records to learn about African Americans in Coles County’s history. They first choose an SRS of records to check their accuracy by visiting the actual gravestones.
(a) Explain how you would use technology or Table D to choose the SRS. Your description should be clear enough for a classmate to obtain your results.
(b) Use your method from (a) to choose the first gravestones.
Aw, rats! A nutrition experimenter intends to compare the weight gain of newly weaned male rats fed Diet A with that of rats fed Diet B. To do this, she will feed each diet to 10 rats. She has available rats from one litter and rats from a second litter. Rats in the first litter appear to be slightly healthier.
(a) If the rats from Litter 1 were fed Diet A, the effects of genetics and diet would be confounded, and the experiment would be biased in favor of Diet A. Explain this statement carefully.
(b) Describe a better design for this experiment.
Look, Ma, no hands! Does talking on a hands-free cell phone distract drivers? Researchers recruit student subjects for an experiment to investigate this question. They have a driving simulator equipped with a hands-free phone for use in the study.
(a) Researchers are considering the design shown in the figure below. What type of design is this?
(b) Explain how blocking could be used to improve the design in (a).
(c) Why is it important to randomly assign the treatments within each block?
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