Question

5. Researchers conducted a study of smartphone use among adults. A cell phone company calmed that IPhone smartphones are more popular with whites (non-Hispanic) than with African Americans. The results of the survey Indicate that of the 232 African American cell phone owners randomly sampled, 5% have an iPhone. Of the 1,343 white cell phone owners randomly sampled, 10% own an iPhone. Test at the 5% level of significance. Is the proportion of white iPhone owners greater than the proportion of African American Phone owners? a State: Ho and Hi, the test statistic, p-value and critical value(s). Solution: Ho: Hj: State whether the test is two-talled, left-talled or right-talled. The value of a = Write the formula for the appropriate test statistic: The value of the P-value= Critical value(s) - b. State the conclusion that addresses the original claim. Solution:

Answer 1

DETE HO 5) a) Let ni= The number of white cell phone owners 1343 na = The number of African American cell phone owners 232 pi= proportion of the number of white cell phone has own owhers an iPhone p2 = proportion of the number of African cell phone owners. an iPhone American has own 0.05 Then A p = nipithap2 nitha = (1343 x 0:10) +(232 x 0.05) 1343+ 232 0.0926 @ -1- ſ = 1-0.09 26 = 0.9074 CS Scanned with CamScannen

Here we have to test there is Ho: Piala i e no significant difference between the proportion of white iPhone owners and the proportion of African American iPhone owners. N: 3 Hi : Pi>P2 ip. The proportion of white iPhone owhers greater than the proportion of African American iPhone owhers The test is right tailed. because alternative hypothesis is right tailed. The value of a = 5% =0.05 Under the hull hypothesis Ho, the test statistic is NCO,1) pi-p2 since ni nz are large ni z = o.10 -0.05 (0.0926 x 0.9074) X 0.0926 X 0.9074) ( 1343 232 z = 2.4261 CS Scanned with CamScannen

Now so p-value is is given as here, we use right failed alternative hypothesis p-value P(Z > 2.4261) From a normal probability integral table have P(Z > 2.4261) = P(Z > 2.43) = 0.0075 we 0.0075 2 = 0.05 p-value Critical value : For the critical value is given as critical value = Z2 = 20.05=1.645 (For right tailed) 6) Since p-value à (level of significance 0.0075 2 0.05 Z 71-645 nce p-value less than level of significance hence reject Ho at 5% level of significa- we reject Ho level of significance and conclude that the proportion of white iPhone owners greater than the proportion of African Americ iphone owners we since 5% -an 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

The following table shows the critical values, Zy of Z at commonly ised level of significance for both two tailed and one tailed tests. Level of Significance Tests 5% i.e. a = 0.05 1% i.e. a = 0.01 10% i.e. a = 0.1 Two tailed -1.645 and -1.96 and 1.96 -2.58 and 2.58 tests 1.645 Right tailed tests 1.645 2.33 1.28 Left tailed tests -1.645 -2.33 -1.28 cs So with Care cs Scanned with CamScanner