Q:

Running Red Lights

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 xbar=1.92 and the standard deviation was sd = 1.83. For this large sample, sd will be close to the population sd, so suppose we know that the pop sd = 1.83.

a) Give a 95% confidence interval for the mean opinion in the population of all licensed drivers.

The 95% confidence interval for the mean option in the population is from 2.042 to 1.798.

b) The distribution of responses is skewed to the right rather than Normal. This will not strongly affect the z confidence interval for this sample. Why not?

The fact that z confidence interval for the sample won’t be strongly affected by the distribution of responses which is skewed to the right is because the sample size is large. If a sample is large, xbar will be close to Normal even if individual measurements are strongly skewed

c) The 880 respondents are an SRS from completed calls among 45,956 calls to randomly chosen residential telephone numbers listed in 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?

The reasons as to why the sample may not represent all licensed drivers are that it only includes in the survey drivers who have telephone numbers, those who do not, do not have any chance of inclusion. Also, only 5029 of 45959 calls were completed. Perhaps those people who were more likely to be caught at home when the survey called had something in common with one another, perhaps for example, seniors, who may not get out as often as other adults and are more likely to be home to receive the survey call.

I feel like I'm not quite right on b) and c)..... am I missing something?

Thanks again So so much.