Homework Sourse1 Past enrollment data indicates that 20 of the students tak
1. Past enrollment data indicates that 20% of the students taking elementary statistics at FHSU have a family size of four people. Is the enrollment in this semester\'s virtual classes significantly more than this claim, as measured statistically? Justify your answer through a formal hypothesis testing procedure on proportions with a 5% level of significance. It is required that you give needed hypotheses and related statistical values below as well as statistical computations to the right (feel free to use the appropriate template from the Excel guide for Unit 3). Then give a proper final interpretive conclusion below based on the statistical measures calculated and related to the context given.
| Number in Family |
| 5 |
| 12 |
| 3 |
| 9 |
| 9 |
| 4 |
| 6 |
| 4 |
| 3 |
| 6 |
| 4 |
| 7 |
| 5 |
| 4 |
| 4 |
| 4 |
| 5 |
| 4 |
| 4 |
| 3 |
| 5 |
| 5 |
| 6 |
| 7 |
| 4 |
| 5 |
| 5 |
| 2 |
| 4 |
| 3 |
| 3 |
| 4 |
| 1 |
| 3 |
| 5 |
| 3 |
| 5 |
| 3 |
| 4 |
| 3 |
| 1 |
| 9 |
| 2 |
| 4 |
| 5 |
| 5 |
| 5 |
| 3 |
| 10 |
| 4 |
| 5 |
| 11 |
| 1 |
| 24 |
| 3 |
| 5 |
| 5 |
| 6 |
| 9 |
| 5 |
| 2 |
| 2 |
| 7 |
| 3 |
| 5 |
| 3 |
| 4 |
| 3 |
| 4 |
| 4 |
| 4 |
| 6 |
| 3 |
| 3 |
| 3 |
Solution
Set Up Hypothesis
Null, H0:P=0.2
Alternate,enrollment in this semester\'s virtual classes significantly more than this claim H1: P>0.2
Test Statistic
count of family size 4 in 75 (x)=18
Number of objects in a sample provided(n)=75
No. Of Success Rate ( P )= x/n = 0.24
Success Probability ( Po )=0.2
Failure Probability ( Qo) = 0.8
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.24-0.2/(Sqrt(0.16)/75)
Zo =0.866
| Zo | =0.866
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.866 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 0.86603 ) = 0.19324
Hence Value of P0.05 < 0.19324,Here We Do not Reject Ho
We don\'t have enough evidence to support enrollment in this semester\'s virtual classes significantly more than this claim
