A Time poll based on a random sample of 1,890 American adults (aged 18 and older

Question

A Time poll based on a random sample of 1,890 American adults (aged 18 and older, living in all 50 U.S. states and District of Columbia) was conducted to study what proportion of Americans' income is falling behind the cost of living. That proportion was estimated to be 58%.

A.) Give a 90% conservative confidence interval for the proportion of all such Americans that would say their income was falling behind the cost of living. Show all work.

B.) The study went on to report the results by age group. If the results were used to make a 90% conservative confidence interval for the proportion of all ‘over 40’ Americans (using only the subset of the 1890 surveyed that are over 40 years old), the corresponding margin of (sampling) error would have been … (Bold one)

Larger                                     Smaller                                                   Cannot tell

C.) The study included the following statement in the footnote: “In addition to sampling error, question wording in surveys can introduce error or bias into the findings of public opinion polls.” Name the type of bias that the wording of the question could introduce. (Bold one)

Selection bias                       Non-response bias                               Response bias

Explanation / Answer

Pr( any random American is falling behind the cost of living) = 0.58

(A) 90% conidence interval = p^ +- sqrt [p^ * (1 - p^)/ N]

= 0.58 +- sqrt [0.58 * 0.42/ 1890]

= 0.58 +- 0.011

= (0.569, 0.591)

(B) as it would only involve the person above 40+ , that would reduce the sample size and that will increase the margin or sampling error "Larger"

(C) THe bias into the findings of public opinion polls are response bias.

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