Chapter 8: Q 53. (page 525)

Teens and their TV sets According to a Gallup Poll report, $64 %$ of teens aged $13$ to $17$ have TVs in their rooms. Here is part of the footnote to this report:
These results are based on telephone interviews with a randomly selected national sample of $1028$ teenagers in the Gallup Poll Panel of households, aged $13$ to $17$ . For results based on this sample, one can say that the maximum error attributable to sampling and other random effects is $\pm 3$ percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.
a. We omitted the confidence level from the footnote. Use what you have learned to estimate the confidence level, assuming that Gallup took an SRS.
b. Give an example of a “practical difficulty” that could lead to bias in this survey.

Expert verified

a. Confidence Level is $95.44 %$

b. Non Response Bias.

Step by step solution

It is given that $n = 1028$

$\hat{p} = 64 % = 0.64$

$E = 3 % = 0.03$

We know that

Marin of Error $E = Z_{α / 2} \times \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}$

Therefore

$0.03 = Z_{α / 2} \times \sqrt{\frac{0.64 (1 - 0.64)}{1028}}$

$Z_{α / 2} = \frac{0.03}{0.01497} = 2$

Probability is determines as: $P (- 2 < Z < 2) = P (Z < 2) - P (Z < - 2)$

$P (- 2 < Z < 2) = 0.9772 - 0.0228$

$P (- 2 < Z < 2) = 0.9544 = 95.44 %$

Confidence Level is $95.44 %$

Non Sampling bias include:

Selection bias, Response bias, Non Response bias.

If we don't have data for everybody, in results in non response bias.

This prevail mostly among teenagers as they are not willing in participation in surveys.

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