Question

In: Statistics and Probability

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported...

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported that entry level wages for male college student graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2020. Assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $.50 of the population mean? a or b?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean? Answer


Solutions

Expert Solution

= sample mean of entry level wages for male college graduates

=sample mean of entry level wages for female college graduates

= entry level wages for male college student graduates =21.68

=entry level wages for female college student graduates=18.80

=2.30

=2.05

a) we have to find probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68

i.e,bound on error =.50

i.e,

we know confidence interval =

therefore ,bound on error =

                        is the z critical value needed for level of confidence.

bound on error =     .50=                      ( is the standard error of mean)

                          

                             =1.5371 , says sample mean of sample size 50 is within 1.5371 standard deviation

required probability= = 2*0.4382 =0.8764 (from z table., shown below)

b)we have to find the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80

bound on error =.50

n=50

.50 =

   .50 =

   =1.72

=2*0.4573 =0.9146

finding area from z table

c) in part b

we can see it has a probability of 0.9146 where part a has a probability of 0.876

d) the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean

i.e probability that   

since we dont seperate tables for normal distribution, convert them into z

   for =.30 , z=-98.85

     for =18.80,z=0

(area to the left of 0)

here is a rough graph of this


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