ECON Statistic homework!

econ210.2015.a.hw1_.pdf

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Name______________________

Econ 210

Homework One

1. In a recent study on SIDS (Sudden Infant Death Syndrome), one hospital collected data on 128 babies who died from SIDS. They then took a random sample of 500 babies who did not die from

SIDS, and they compared the two groups with respect to several variables (e.g. did the child sleep

on his/her stomach, birth weight, time of year, whether the mother smoked, whether she breast-

fed, etc.). One physician noted that 63% of the SIDS babies had mothers that smoked during

pregnancy, whereas only 26% of the control babies had mothers who smoked during pregnancy.

From this evidence, can we conclude that smoking during pregnancy is a likely cause of SIDS in

babies? Explain, and give a concrete example.

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2. In 1948 the pollster George Gallup used something called quota sampling to (incorrectly) predict that Thomas Dewey would beat Harry Truman in the presidential election. [In quota sampling a

population is first segmented into mutually exclusive sub-groups or strata, just as in stratified

random sampling, then judgment is used to select the subjects or units from each segment].

Discuss the problem with the approach to sampling taken by Gallup.

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3. Recently Ed Schultz, a political contributor for MSNBC, polled his audience on the “Ed Show” asking:

Are the increasing gas prices the fault of President Obama? The results of the cell

phone poll were as follows: Yes--12%; No--88%.

What are the biases that this poll is subject to?

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4. Consider a population of N = 5 units, labeled A, B, C, D, E. Consider a simple random sampling design with a random size n = 3.

a. List every possible sample of size n = 3. ______________________________________________________________________________

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b. If this population is sampled using simple random sampling, what is the probability that the sample {A,B,C} will be selected?

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5. We wish to conduct a survey to estimate the proportion, p, of individuals in the population who have tested positive for HPV. A simple random sample of 1000 individuals is chosen. Each

person is then supplied with a coin and given the following instructions: Flip the coin in secret, if

the coin comes up heads, answer question A below. If it comes up tails, answer question B.

Question A: To your knowledge, are you infected with HPV?

Question B: Is your zodiac sign included in the following set? {Cancer, Leo, Virgo}

Of the 1000 sampled individuals, suppose 170 respond “Yes.”

a. How many people would expect to answer A, and how many would you expect to answer B? ______________________________________________________________________________

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b. Of the people who answered B, how many people would you expect to answer “yes”? ______________________________________________________________________________

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c. Using you answer to (b) estimate the percentage, p, of people in the population that are carriers of HPV and are aware of their condition?

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