Question

2. (18.02) 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 787 respondents was x⎯⎯⎯ = 1.89 and the standard deviation was s = 1.93. For this large sample, s will be close to the population standard deviation σ, so suppose we know that σ = 1.93.

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

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

No or Yes

Answer #1

Z score for 95% confidence interval = Z_{0.025} =
1.96

Confidence interval

= (1.89 + 0.13)

= (1.76 , 2.02)

No, it will not affect the z confidence interval for this sample. Because the sample size is very large so as per central limit theorem the sampling distribution will be normal distribution.

(18.02) A survey of licensed drivers inquired about running red
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s = 1.99. For this large sample, s will be close to the population
standard deviation s, so suppose we know that s = 1.99.
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