Use the sample data and confidence level given below to complete parts (a) through (d). A research
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Question:
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll,n=1079 and x=556 who said "yes." Use a 95% confidence level.
a) Find the best point estimate of the population proportion p.
b) Identify the value of the margin of error E.
c) Construct the confidence interval.
d) Write a statement that correctly interprets the confidence interval.
Positive z Scores Standard Normal (z) Distribution: Cumulative Area from the Left
Positive z Scores | |||||||||||
Standard Normal (z) Distribution: Cumulative Area from the Left | |||||||||||
z | 0 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | z |
0 | 0.5 | 0.504 | 0.508 | 0.512 | 0.516 | 0.5199 | 0.5239 | 0.5279 | 0.5319 | 0.5359 | 0 |
0.1 | 0.5398 | 0.5438 | 0.5478 | 0.5517 | 0.5557 | 0.5596 | 0.5636 | 0.5675 | 0.5714 | 0.5753 | 0.1 |
0.2 | 0.5793 | 0.5832 | 0.5871 | 0.591 | 0.5948 | 0.5987 | 0.6026 | 0.6064 | 0.6103 | 0.6141 | 0.2 |
0.3 | 0.6179 | 0.6217 | 0.6255 | 0.6293 | 0.6331 | 0.6368 | 0.6406 | 0.6443 | 0.648 | 0.6517 | 0.3 |
0.4 | 0.6554 | 0.6591 | 0.6628 | 0.6664 | 0.67 | 0.6736 | 0.6772 | 0.6808 | 0.6844 | 0.6879 | 0.4 |
0.5 | 0.6915 | 0.695 | 0.6985 | 0.7019 | 0.7054 | 0.7088 | 0.7123 | 0.7157 | 0.719 | 0.7224 | 0.5 |
0.6 | 0.7257 | 0.7291 | 0.7324 | 0.7357 | 0.7389 | 0.7422 | 0.7454 | 0.7486 | 0.7517 | 0.7549 | 0.6 |
0.7 | 0.758 | 0.7611 | 0.7642 | 0.7673 | 0.7704 | 0.7734 | 0.7764 | 0.7794 | 0.7823 | 0.7852 | 0.7 |
0.8 | 0.7881 | 0.791 | 0.7939 | 0.7967 | 0.7995 | 0.8023 | 0.8051 | 0.8078 | 0.8106 | 0.8133 | 0.8 |
0.9 | 0.8159 | 0.8186 | 0.8212 | 0.8238 | 0.8264 | 0.8289 | 0.8315 | 0.834 | 0.8365 | 0.8389 | 0.9 |
1 | 0.8413 | 0.8438 | 0.8461 | 0.8485 | 0.8508 | 0.8531 | 0.8554 | 0.8577 | 0.8599 | 0.8621 | 1 |
1.1 | 0.8643 | 0.8665 | 0.8686 | 0.8708 | 0.8729 | 0.8749 | 0.877 | 0.879 | 0.881 | 0.883 | 1.1 |
1.2 | 0.8849 | 0.8869 | 0.8888 | 0.8907 | 0.8925 | 0.8944 | 0.8962 | 0.898 | 0.8997 | 0.9015 | 1.2 |
1.3 | 0.9032 | 0.9049 | 0.9066 | 0.9082 | 0.9099 | 0.9115 | 0.9131 | 0.9147 | 0.9162 | 0.9177 | 1.3 |
1.4 | 0.9192 | 0.9207 | 0.9222 | 0.9236 | 0.9251 | 0.9265 | 0.9279 | 0.9292 | 0.9306 | 0.9319 | 1.4 |
1.5 | 0.9332 | 0.9345 | 0.9357 | 0.937 | 0.9382 | 0.9394 | 0.9406 | 0.9418 | 0.9429 | 0.9441 | 1.5 |
1.6 | 0.9452 | 0.9463 | 0.9474 | 0.9484 | 0.9495 | 0.9505 | 0.9515 | 0.9525 | 0.9535 | 0.9545 | 1.6 |
1.7 | 0.9554 | 0.9564 | 0.9573 | 0.9582 | 0.9591 | 0.9599 | 0.9608 | 0.9616 | 0.9625 | 0.9633 | 1.7 |
1.8 | 0.9641 | 0.9649 | 0.9656 | 0.9664 | 0.9671 | 0.9678 | 0.9686 | 0.9693 | 0.9699 | 0.9706 | 1.8 |
1.9 | 0.9713 | 0.9719 | 0.9726 | 0.9732 | 0.9738 | 0.9744 | 0.975 | 0.9756 | 0.9761 | 0.9767 | 1.9 |
2 | 0.9772 | 0.9778 | 0.9783 | 0.9788 | 0.9793 | 0.9798 | 0.9803 | 0.9808 | 0.9812 | 0.9817 | 2 |
2.1 | 0.9821 | 0.9826 | 0.983 | 0.9834 | 0.9838 | 0.9842 | 0.9846 | 0.985 | 0.9854 | 0.9857 | 2.1 |
2.2 | 0.9861 | 0.9864 | 0.9868 | 0.9871 | 0.9875 | 0.9878 | 0.9881 | 0.9884 | 0.9887 | 0.989 | 2.2 |
2.3 | 0.9893 | 0.9896 | 0.9898 | 0.9901 | 0.9904 | 0.9906 | 0.9909 | 0.9911 | 0.9913 | 0.9916 | 2.3 |
2.4 | 0.9918 | 0.992 | 0.9922 | 0.9925 | 0.9927 | 0.9929 | 0.9931 | 0.9932 | 0.9934 | 0.9936 | 2.4 |
2.5 | 0.9938 | 0.994 | 0.9941 | 0.9943 | 0.9945 | 0.9946 | 0.9948 | 0.9949 | 0.9951 | 0.9952 | 2.5 |
2.6 | 0.9953 | 0.9955 | 0.9956 | 0.9957 | 0.9959 | 0.996 | 0.9961 | 0.9962 | 0.9963 | 0.9964 | 2.6 |
2.7 | 0.9965 | 0.9966 | 0.9967 | 0.9968 | 0.9969 | 0.997 | 0.9971 | 0.9972 | 0.9973 | 0.9974 | 2.7 |
2.8 | 0.9974 | 0.9975 | 0.9976 | 0.9977 | 0.9977 | 0.9978 | 0.9979 | 0.9979 | 0.998 | 0.9981 | 2.8 |
2.9 | 0.9981 | 0.9982 | 0.9982 | 0.9983 | 0.9984 | 0.9984 | 0.9985 | 0.9985 | 0.9986 | 0.9986 | 2.9 |
3 | 0.9987 | 0.9987 | 0.9987 | 0.9988 | 0.9988 | 0.9989 | 0.9989 | 0.9989 | 0.999 | 0.999 | 3 |
3.1 | 0.999 | 0.9991 | 0.9991 | 0.9991 | 0.9992 | 0.9992 | 0.9992 | 0.9992 | 0.9993 | 0.9993 | 3.1 |
3.2 | 0.9993 | 0.9993 | 0.9994 | 0.9994 | 0.9994 | 0.9994 | 0.9994 | 0.9995 | 0.9995 | 0.9995 | 3.2 |
3.3 | 0.9995 | 0.9995 | 0.9995 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9997 | 3.3 |
3.4 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9998 | 3.4 |
3.50 and up | 0.9999 | 3.50 and up | |||||||||
z | 0 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | z |
Note: For values of z above 3.49, use 0.9999 for the area. | |||||||||||
*Use these common values that result from interpolation: | |||||||||||
z score | Area | ||||||||||
1.645 | 0.95 | ||||||||||
2.575 | 0.995 | ||||||||||
Common Critical Values | |||||||||||
Confidence Level | Critical Value | ||||||||||
0.9 | 1.645 | ||||||||||
0.95 | 1.96 | ||||||||||
0.99 | 2.575 |
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