Question

In: Statistics and Probability

A random sample of 35 standard metropolitan statistical areas (SMSAs) was selected and the ratio (per...

  1. 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 ago
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