Question

Employment in CaliforniaEach month the government releases unemployment

statistics. The stated unemployment rate doesn’t include people who choose not to be employed, such as retirees. Based on a random sample of $1000$California adults, a $99\%$confidence interval for the proportion of all California adults employed in the workforce is $0.532\mathrm{to}0.612.$

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 untruthful answers might lead to bias in this survey. Does the stated margin of error account for this possible bias?

Short answer

a. $99\%$samples have $99\%$confidence interval that has correct proportion of all employees.

b. The drawbacks are reduction in margin of error by increasing sample size and decreasing confidence level.

c. When values are different from true value, it is response bias. Margin of error is not included here.

Step-by-step solution

Given Information

Sample of $1000$California adults is given. $99\%$confidence interval is given.

Range is$0.532\text{to}0.612$.

Explaining Confidence Interval

$99\%$samples have $99\%$confidence that has correct proportion of California adults employed.

Drawbacks of Action

Margin of Error is reduced by:

• Decrease in Confidence Level: There is less confidence that confidence interval has correct population parameter. It has less values for true parameter of population.
• Increase in Sample Size: It will give more correct estimate. Nut it is costly and time consuming.

Response Bias and Margin of Error

Response bias use a method that obtain different values than true values.

It gives overestimate or underestimate of true population parameters and results in bias.

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