In August 2011 59 of employed adults in the United States re

In August 2011, 59% of employed adults in the United States reported that basic mathematical skills were critical or important to their job. The director of the Career Center at a 4-year college believes that this percentage has increased because of all the new technology use in the workplaces. In order to prove his point, he takes a random sample of 280 employed adults and finds that 65% of them feel that basic mathematical skills are critical or important to their job.

Is this enough evidence for the director to support his belief that more employed adults think that mathematical skills are important in their jobs? Use a 5% significance level.

1)      What type of hypothesis test is needed? What distribution should be used? Why?

2)      State the two hypotheses here.

H_o :                                            H₁ :

3)      Find the critical value and the test statistics. State them here.

4)      Is this a right, left or two-tailed test? Sketch a normal curve, mark the critical value and test statistics and shade the rejection region on the curve.

5)      Use your calculator to find the P value. State it here.

6)      Do we reject or not reject the null hypothesis? Is there sufficient evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased? If you were the director, what kind of suggestions would you include in your report to your supervisor?

Solution

1)
Z-Test For Proportion
2)
Set Up Hypothesis
Null, H0:P=0.59
Alternate, H1: P>0.59
3)
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
Test Statistic
No. Of Success chances Observed (x)=182
Number of objects in a sample provided(n)=280
No. Of Success Rate ( P )= x/n = 0.65
Success Probability ( Po )=0.59
Failure Probability ( Qo) = 0.41
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.65-0.59/(Sqrt(0.2419)/280)
Zo =2.0413
| Zo | =2.0413
4)
It is right tailed test

5 & 6)
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.04133 ) = 0.02061
Hence Value of P0.05 > 0.02061,Here we Reject Ho

It is proven that director to support his belief that more employed adults think that mathematical skills are important in their jobs