Question

California’s traffic People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of $572$employed California adults, a $90\%$confidence interval for the average travel time to work for all employed California adults is $23$minutes to $26$ minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

Short answer

a. $90\%$of all samples have $90\%$confidence interval that has correct average travel times.

b. It increases sample size and decreases confidence level.

c. It results after not having appropriate data for everybody.

Step-by-step solution

Given Information

Sample of $572$California adults is given.

$90\%$confidence interval is given.

Average time is$23-26$minutes.

Explaining Confidence Level

$90\%$of all samples has $90\%$ confidence interval that contain right average travel time for all employed adults of California.

Drawbacks of these Action

It decreases Margin of Error as:

• Increase in Sample Size: It give more data about population and we obtain correct estimate. It is expensive and time consuming to collect data.
• Decrease in Confidence Level: Confidence interval having correct population interval is less confident. It has less possible values for true population parameter. Hence, it is less confident about confidence interval having correct population parameter.

Non Response Bias

When there is not enough data for everybody in the sample, it results in non response bias. Persons whose data is not available results in overestimating or underestimating the true population and cause bias.

Margin of Error is not included here as it accounts for possible variation only.