Question

11:00 y = -0.96 - 90.21 x 2 points Use the frequency table below to find the population variance. * Price F 60 - 66 50 67 - 73 60 74 - 80 10 81 - 87 90 Your answer 2 points In a two-tailed test, If the current population mean is 54 and a sample of size 60 has a mean of 57, find the p-value given that the population standard deviation is 8.49 * Your answer 2 points Usina the box plot below. Find the III >

Please Solve As soon as
Thank's
Abdul-Rahim Taysir

Answer 1

Population Variance :

First find mid points (M)

$M=\frac{Upper\: Limit+Lower\: Limit}{2}$

M 66 + 60 2 63

$M=\frac{73+67}{2}=70$

M 74 + 80 2 = 77

M 87 + 81 2 84

Price F M F*M 60-66 50 63 67-73 60 10 90 70 77 (M-74.6667)^2 F*(M-74.6667)^2 3150 136.1118889 6805.594445 4200 21.77808889 1306.685333 770 5.44428889 54.4428889 7560 87.11048889 7839.944 74-80 81-87 84 Total 210 15680 16006.66667

$\mu =\frac{\sum (F*M)}{\sum F}=\frac{15680}{210}=74.6667$

Variance :

$\sigma ^2=\frac{\sum F(M-\mu)^2}{\sum F}=\frac{16006.66667}{210}=76.22$

Population variance is 76.22

Que.2

$\sigma=8.49$

$\mu =54$

n = 60

$\bar{x}=57$

Z score :

$Z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}=\frac{57-54 }{\frac{8.49}{\sqrt{60}}}=\frac{3}{1.096054287 }=2.74$

Z = 2.74

Find P value Using z table or use excel command =NORMSDIST(2.74)

P( Z< 2.74) = 0.9969

2*P( Z>2.74 ) =2*(1-P( Z< 2.74) )=2*(1- 0.9969)=2*0.0031= 0.0062

Answer : For two tailed test p value is 0.0062

Z table:

.00 .01 N .02 .03 104 105 .06 107 ,08 109 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 12 1.3 1.4 1.5 1.6 1.7 18 19 2.0 2.1 2.2 23 15000 5040 15080 15120 5160 1519 5239 15398 15438 15478 1.5517 5557 15596 5636 15793 15832 1.5871 910 15948 15987 16026 .6179 16217 .6255 .6293 16331 6368 .6406 6554 .6591 6628 1.6664 6700 16736 6772 .6915 16950 .6985 7019 17054 17098 17123 7257 7291 17324 7357739 47422 7454 7580 7611 7642 7673 7704 734 764 17881 7910 - 7939 17967 7995,8023 .8051 18159 8186 8212 18238 18264 8289 8315 1413 184388 18461 18485 18508 18531 18554 643 8665 18686 18708 8729 .8749 18770 18849 18869 18888 189078925 18944 18962 19032 19049 1.9066 19082 9099 19115 19131 9192 19207 9222 19236 9251 19265 9279 9332 19345 19357 19370 19382 19394 19406 19452 19463 19474 19484 19495 19505 19515 19554 19564 19573 19582 19591 19599 19608 19641 19649 19656 19664 19671 19678 19686 19713 19719 19726 19732 19738 19744 19750 19772 1.9778 9783 9798 19793 19798 19803 19821 19826 19830 198349838 19842 19846 19861 19864 19868 19871 19875 19878 19881 19893 19896 19898 19901 9904 19906 19909 19918 19920 19922 19925 9927 19929 19931 19938 19940 19941 19943 19945 19946 19948 19953 19955 19956 19957 19959 19960 19961 19965 19966 19967 19968 9969 19970 19971 19974 19975 19976 1997 19977 19978 19979 19981 19982 19982 19983 19984 19984 19985 19987 19987 19987 1998 998 19989 19989 19990 19991 19991 19991 19992 19992 19992 19993 19993 9994 19994 9994 19994 9994 19995 9995 19995 19996 19996 19996 9996 19997 19997 19997 19997 19997.9997 9997 5279 5675 16064 .6443 6808 17157 17486 794 18078 18340 18577 18790 18980 19147 19292 9418 19525 19616 19693 19756 19808 19850 15319 5359 5714 5753 .6103 .6141 .6480 .6517 .6844 .6879 17190 17224 7517 7549 7823 7852 18106 8133 18365 8389 18599 18621 1810 8830 8997 9015 9162 9177 9306 9319 19429 19441 19535 19545 19625 19633 19699 9706 19761 19767 19812 19817 19854 19857 19887 19890 9913 9916 19934 9936 19951 19952 19963 19964 19973 19974 19980 19981 19986 19986 19990 9990 19993 9993 19995 19995 19996 9997 19997 9998 2.4 2.5 2.6 2.7 2.8 29 3.0 3.1 3.2 3.3 3.4 19884 19911 19932 19949 19962 19972 1.9979 19985 19989 19992 9995 19996 19997