Question

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 915 respondents was x¯¯¯ = 1.93 and the standard deviation was s = 1.66. For this large sample, s will be close to the population standard deviation s, so suppose we know that s = 1.66. 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 Yes

Answer 1

Answer:

Given,

xbar = 1.93

n = 915

s = 1.66

Here for the 95% confidence interval , z critical value is 1.96

Interval = xbar +/- z*s/sqrt(n)

substitute the known values

= 1.93 +/- 1.96*1.66/sqrt(915)

= 1.93 +/- 0.1076

= (1.93 - 0.1076 , 1.93 + 0.1076)

= (1.8224 , 2.0376)

Here we can say , No , Due to that the sample size is too high to apply central limit theorem. It says that the sample means follows the normal distribution irrespective of what distribution population has.