Question
In: Statistics and Probability
A random sample of 35 standard metropolitan statistical areas (SMSAs) was selected and the ratio (per...
- A random sample of 35 standard metropolitan statistical areas (SMSAs) was selected and the ratio (per 1,000) of registered voters to the total number of persons 18 years and over was recorded in each area. Use the sample data given to test the research hypothesis that the population average ratio is greater than 675, last year’s average ratio. Use =.025.
|
802 |
497 |
653 |
600 |
729 |
812 |
743 |
|
751 |
730 |
635 |
605 |
760 |
681 |
811 |
|
807 |
747 |
728 |
561 |
696 |
710 |
735 |
|
641 |
848 |
672 |
740 |
818 |
725 |
646 |
|
694 |
854 |
674 |
683 |
695 |
803 |
632 |
Solutions
Expert Solution
#Null and alternative hypothesis are
H0:
=675
Ha:>675
| x | (x-xbar)^2 | |
| 802 | 8110.289 | |
| 751 | 1525.4604 | |
| 807 | 9035.8604 | |
| 641 | 5032.889 | |
| 694 | 321.94612 | |
| 497 | 46200.432 | |
| 730 | 326.06041 | |
| 747 | 1229.0033 | |
| 848 | 18511.546 | |
| 854 | 20180.232 | |
| 653 | 3474.2604 | |
| 635 | 5920.2033 | |
| 728 | 257.83184 | |
| 672 | 1595.4318 | |
| 674 | 1439.6604 | |
| 600 | 12531.203 | |
| 605 | 11436.775 | |
| 561 | 22783.746 | |
| 740 | 787.20327 | |
| 683 | 837.68898 | |
| 729 | 290.94612 | |
| 760 | 2309.489 | |
| 696 | 254.17469 | |
| 818 | 11248.118 | |
| 695 | 287.06041 | |
| 812 | 10011.432 | |
| 681 | 957.46041 | |
| 710 | 3.7746939 | |
| 725 | 170.48898 | |
| 803 | 8291.4033 | |
| 743 | 964.54612 | |
| 811 | 9812.3176 | |
| 735 | 531.63184 | |
| 646 | 4348.4604 | |
| 632 | 6390.8604 | |
| sum | 24918 | 227409.89 |
| mean | 711.9428571 | |
| xbar | sum(x)/n | 711.94286 |
| s | sqrt(sum(x-xbar)^2/n-1) | 81.783409 |
xbar=711.94286
s=sample standard deviation=81.783
#test statistics=(xbar-)/s/sqrt(n)
=(711.94286-675)/81.783/sqrt(35)
=2.6723
#degree of freedom =n-1=34
P-value=P(t34>2.673)
P-value=0.0057---- using t-table with corresponding df=34
P-value<0.025 hence reject Ho
#Conclusion:
reject Ho and Conclude that there is sufficent evidence that population average ratio is greater than 675,
orchestra answered 2 years agoRelated Solutions
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