#22) A survey of licensed drivers inquired about running red lights. One questio

Question

#22) A survey of licensed drivers inquired about running red lights. One question asked, "Of every ten motorists who run a red light, about how many do you think will be caught?" The mean result for 880 respondents was x¯ = 1.92 and the standard deviation was s = 1.83.2 For this large sample, s will be close to the population standard deviation , so suppose we know that = 1.83.

A) Give a 95% confidence interval (±0.01) for the mean opinion in the population of all licensed drivers:_______ ± _________ .

B) The distribution of responses is skewed to the right rather than Normal. Will it strongly affect the z confidence interval for this sample?

C) The 880 resopndents are an SRS from completed calls among 45,956 calls to randomly chosen residential telephone numbers listed in the telephone directories. Only 5029 of the calls were completed. This information gives two reasons to suspect that the sample may not represent all licensed drivers. What are these reasons?

Explanation / Answer

A)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)                              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    1.92          

z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    1.83          
n = sample size =    880          
              
Thus,              

Margin of Error E =    0.120908782          

Hence, the confidence interval is

1.92 +/- 0.120908782 [ANSWER]

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b)

No, as the sample size is large enough. By central limit theorem, the sample means will still be approximately normal.

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c)

It may introduce some sampling bias becasue

1. Only those with telephones can be surveyed
2. Only those with completed calls are sampled, so that could indicate sampling only those with clear signal in their homes, or those who have time to complete the survey.

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