Question

In March 2014, Harris Interactive conducted a poll of a random sample of 2234 adult Americans 18 years of age or older and asked, "which is more annoying to you, tailgaters or slow drivers who stay in the passing lane?" Among those surveyed, 1184 were more annoyed by tailgaters

a) Explain why the variable of interest is qualitative with two possible outcomes. What are the two outcomes?

b) Verify the requirements for constructing a 90% confidence intervsl for the population proportion of all adult Americans who are more annoyed by tailgaters than slow drivers in the passing lane.

c)Construct a 90% confidence interval for the population proportion of all adult Americans who are more annoyed by tailgaters than slow drivers in the passing lane.

Answer 1

(a) The variable of interest is 'what cases annoyance'?. This is not a value like 15 cm, or 20 years etc. The anser to this question has 2 outcomes are 'tailgaters' or 'slow drivers' which are not numerical (quantitative) in nature and are qualitative.

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(b) The Conditions to be verified

1) Random sampling- This condition is met as it is mentioned that it is random sampling.

2) = 1184/2234 = 0.53

n * = 2234 * 0.53 = 1184 and n * (1-) = 2234*0.47 = 1050 are both greater than 10

3) Individual observations can be considered independent as 2234 drivers aged 18 years or older will have a population greater than 10 times 2234 (greater than 22340), hence the sample size is < 10%.

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(c) The CI is given by ME

= 1184/ 2234 = 0.57, 1 - = 0..43, n = 223, = 0.10

The Zcritical (2 tail) for = 0.10, is 1.645

The Confidence Interval is given by ME, where

The Lower Limit = 0.53 - 0.017 = 0.513

The Upper Limit = 0.53 + 0.017 = 0.547

The Confidence Interval is (0.513 , 0.547)