Question

Wage information collected by the Census Bureau shows the number of workers being paid at or below minimum wage between 1979 to 2017. The survey runs monthly with sample sizes of 60,000 men and 60,000 women participants.

• The wages of men paid at or below minimum wage showed a mean of 1393 workers and a std. deviation of 589 workers.

• The wages of women paid at or below minimum wage showed a mean of 2511 workers and a std. deviation of 1107 workers.

1. Construct a 95% confidence interval to estimate the true population mean of men that are being paid at or below minimum wage:

   <     (enter a variable or word) <     (remember to round up to nearest integers)

2. Is this a t-distribution or z-distribution? (answer 't' or 'z')

3. What are the critical values associated with your given significance level α?  (separate your answers by comma and round to 2 decimals)

4. What is the margin of error for men workers?    (remember to round up to nearest integer)

5. Construct a 95% confidence interval to estimate the true population mean of women that are being paid at or below minimum wage:

   <     (enter a variable) <   (remember to round up to nearest integers)

6. What is the margin of error for women workers?    (remember to round up to nearest integer)

Answer 1

Sol:

1).

95% of Confidence interval =

Here x̅ = 1393

s= 589

n = 60,000

z = 1.96

Confidence interval = ( 1388,1398)

2).

Answer is  "Z".

Because The sample sizes n= 60,000 being the large enough even the population variance is unknown here.

The distribution of test-statistic z can be approximated by N( 0, 1 ) distribution. i.e. Z-test.

3).

Given

alpha = 95%

Crtical values = ±1.96

4).

Margin of Error =

E = 4.71

5).

95% of Confidence interval =

Here

Here x̅ = 2511

s= 1107

n = 60,000

z = 1.96

Confidence interval = ( 2502,2520).

6).

Margin of Error =

E = 8.86