Question

1.) Voting records show that 61% of eligible voters actually did vote in a recent presidential election. In a survey of 1002 people, 70% said that they voted in that election.

1. Use the survey results to test the claim that the percentage of all voters who say that they voted is equal to 61%.
2. Test the claim by constructing an appropriate confidence interval.   
3. What are the null and alternative hypotheses?
4. What is the value of = significance level?
5. Is the test two-tailed, left-tailed or right-tailed?
6. What is the test statistic and what is its distribution?
7. What is the value of the test statistic?
8. What is the P-value?
9. What is (are) the critical value(s)?
10. How would you state a conclusion that addresses the original claim?

Answer 1

- Here we have given that n = 1002 pe proportion of people in survey of 1002 that they voted in that election P= Proportion of people that they voted that election p = 0.70 061 = 0.61 6) Here we have to test le Ho: P = 0.61 The percentage of all voters who say that they voted in that election is equal to 61% H. P & 0.61 ie the percentage of all voters that they voted in that election is not equal to 61% who say Know 100(1-2)/ confidence internal for population proportion is given as ( p. 24/ 2 / pci-pl p+2442 leclip we want to find 95% confidence interval for population proportion. zote = 20.05= 20.025 = 1.96 CS Scanned with CamScannen

lower bound for pa 2012 Teatre 0.70 - (1.96x 0.70 xo 36 100 2 0.6716 1 bound upper for pt Z42 PCI-pl 070+ (1.96x 01080 30 1002 = 0.7284 95% confidence interval for interval for population proportion is (0.6716 0.7284) is not Hence out p=0.61 in the 95% confidence interval hence we reject reject the null hypothesis with 95% confidence and claim that the percentage of all volers that they vote in that election is not & equal to 61% who say CS Scanned with CamScannen

c) Here we have to test Но P=0.61 Vis HI: PE 0.61 d) Here we use level of significance - 20.05 tailed test el It is E) Under Ho the test statistic is Z P-P > N(0,1) for large n V poln ( 0 = 1-P) १) The value of test statistic is 2 = 0.70-0.61 0.61x11-0-61) poo 1002 5.8 409 h) The p-value of two-tailed z test is given as 2 x P(Z > 5.84) p-value- 2x PLZ 205.84) or p-value 2 x 0.0 005 = 0.0000 CS Scanned with CamScanner

for L=0.05 are i) The critical values and 1.96 -1.96 j) Now p-value ex (level of significance) O ooool Lo.05 calculated Izl is greater than 196 hence reject the null hypothesis Ho at 5% level of significance and conclude that the percentage of all voters, who say that they voted that election is not equal to 61% CS Scanned with CamScanner
z table as follows:

Area 0.02 0.09 z 0.0 0.1 0.2 0,3 0.4 0.5 0.6 0.7 0.8 0.9 1,0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0 0.01 0.04 0.05 0.06 0.07 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.6179 0.6217 0,6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.6554 0.6591 0.6626 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.6915 0.6950 0.6985 0.7019 0.7054 0.70BB 0.7123 0.7157 0.7190 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.6238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.8413 0.8438 0.8461 0.8485 0.8508 0,8531 0.8554 0.8577 0.8599 0.8621 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.3810 0.8830 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9508 0.9616 0.9625 0.9633 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9612 0.9817 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9951 0.9962 0.9963 0.9964 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9996 0.9996 0.9886 0.9996 0.9995 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 2.1 2.2 2.3 24 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4