Question

(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 934 respondents was x¯¯¯ = 1.96 and the standard deviation was 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.

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? Yes or No

Answer 1

Answer)

As the population standard deviation is known here

We can use standard normal z table to estimate the interval

N = 934

Confidence level = 95%

S.d = 1.99

Mean = 1.96

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*S.D/√N = 1.96*1.99/√934 = 0.12762498664

Interval is given by

(Mean - MOE, Mean + MOE)

(1.83237501335, 2.08762498664)

According to the central limit theorem, if sample size is large enough > 30, we can assume.the normality

So no, it wont affect the z interval as sample size is large