Question

A nutrition consulting company created an education program to increase the calcium intake in children ages 9 to 13. To measure the effectiveness of the program, an analyst performs an experiment in which 198 children are assigned randomly to either the control group (no education) or the education group. The average daily dietary calcium intake is calculated from 3-day diet records. Before the analyst can perform hypothesis tests, she needs to know if the variances of the two groups are equal or not so that she can determine what type of hypothesis test to use (Parametric or Non-Parametric). Use the Equal_Variances.MTW data file to perform a test of equal variances and determine if the two groups have equal variances.

Calcium   Group
646.718938358203   Control
1120.66884477362   Control
1067.25197943551   Control
911.624742599909   Control
898.895367854688   Control
1088.41268757664   Control
1271.48521000362   Control
729.383778742021   Control
983.859574875372   Control
905.044576198034   Control
546.071919866484   Control
715.568075723858   Control
966.077942357849   Control
1099.84663143188   Control
1035.60968971358   Control
698.565902695813   Control
935.751007584594   Control
865.305220486097   Control
1232.5438640389   Control
899.699184074123   Control
1259.54465321706   Control
1327.13626005019   Control
954.862824311777   Control
683.096757798792   Control
839.797920019532   Control
608.791819237845   Control
1063.60241792683   Control
1287.18586964095   Control
910.147706316883   Control
1049.07762406466   Control
336.23327683719   Control
520.921030893244   Control
807.353805936021   Control
1429.69059848441   Control
461.065913514199   Control
954.824551355506   Control
359.473499314655   Control
1150.06303841653   Control
722.74667000439   Control
1069.23255942596   Control
883.213304316289   Control
829.472760293924   Control
1341.87329441388   Control
567.274109385454   Control
702.367646659113   Control
872.716285426422   Control
320.781003645417   Control
788.717898193134   Control
795.270919272801   Control
1174.45273674766   Control
684.286947645718   Control
1197.97911103269   Control
871.59081913733   Control
558.624799529507   Control
682.764196350705   Control
425.366614281267   Control
364.69994726096   Control
502.306961956663   Control
1010.01657543712   Control
721.851178257459   Control
783.754839352849   Control
941.094730484834   Control
681.53021550534   Control
714.32289464054   Control
546.596093290559   Control
701.966170386693   Control
407.506044392304   Control
649.724734020368   Control
1013.90578437461   Control
487.251009881645   Control
1125.02859624156   Control
801.070963955146   Control
913.505590201886   Control
555.303404529004   Control
626.344387491074   Control
1118.94696799092   Control
800.133615896361   Control
817.559677766571   Control
677.293702889565   Control
577.136195347531   Control
797.011616506485   Control
574.405945643188   Control
673.860788692258   Control
640.154335629558   Control
726.754006577547   Control
871.837981179152   Control
554.916353340325   Control
817.765305093996   Control
1023.53922905079   Control
778.440001362496   Control
1033.75166394017   Control
863.072814876006   Control
482.929204765678   Control
757.717697206004   Control
961.759393491617   Control
752.079104746515   Control
1099.64642788733   Control
675.889347527723   Control
1212.86127908923   Education
1043.58183576511   Education
1001.02467542113   Education
1433.66666503496   Education
1242.36295439191   Education
1005.38027642987   Education
1310.90065971212   Education
1041.10713152717   Education
1039.0993753776   Education
989.203765312553   Education
1152.30889717592   Education
1069.27412733254   Education
1222.95571155341   Education
937.227131758598   Education
1231.97180255013   Education
1288.30956894443   Education
934.641799963676   Education
951.519397164352   Education
880.150953760751   Education
1337.12934460539   Education
1150.20746167798   Education
1425.89368404825   Education
1107.11421120659   Education
1347.23302140043   Education
1057.36151355459   Education
807.630671558523   Education
1393.46121505187   Education
1265.1805592468   Education
974.043747071429   Education
1043.12557050404   Education
1101.07770090962   Education
1100.36253237378   Education
1269.85555459434   Education
1117.16284246044   Education
1273.25093388539   Education
918.442747376225   Education
1154.10000749998   Education
1031.95095005953   Education
1196.46758876627   Education
1167.80704978808   Education
652.41252737704   Education
705.073189240597   Education
1160.07605005674   Education
1215.92689429818   Education
1269.67988395412   Education
992.532061947513   Education
893.230651173659   Education
1040.01683270812   Education
998.869581034692   Education
1292.45533515759   Education
985.769272826702   Education
1062.04422672555   Education
913.108875584995   Education
907.570870445983   Education
1155.11840910918   Education
1517.17232610728   Education
982.892509295403   Education
1033.85082546014   Education
1298.96779458962   Education
713.114373419194   Education
751.241491805589   Education
1254.81650540777   Education
1168.4696785167   Education
939.693919974494   Education
1167.76178576134   Education
1190.6386610843   Education
1040.1220559694   Education
1502.88356884033   Education
1128.50289428548   Education
1034.90807572673   Education
1188.42295410829   Education
1291.87796136998   Education
1279.34817295133   Education
1283.98058261949   Education
1022.57252075428   Education
1117.19876078909   Education
931.503937304133   Education
1233.74375961551   Education
1469.41522092619   Education
716.816245140364   Education
1052.92091190376   Education
1347.81770450501   Education
1371.16163167695   Education
1081.63622765917   Education
961.941039301563   Education
1433.1882590068   Education
1241.81563105457   Education
1060.29846142643   Education
1011.40603523059   Education
1153.07766725887   Education
963.551933580363   Education
1082.42275789195   Education
1057.30148554377   Education
1321.56941906484   Education
766.866676879017   Education
1117.46167012446   Education
934.032532507596   Education
1309.17920918181   Education
1284.76821777109   Education
993.098270535973   Education

Answer 1

Using Minitab, Summary of the data is to find data is parametric or non-parametric:

For a Parametric specifications: A) Each group data must be greater than 20, B)Distribution of data must be normal and C) Do not have Ordinal, ranked data or Outliers data that can't remove observations

Summary of each group:

Distribution of data is normal and no outliers with in the dataset.

Distribution of data is normal and no outliers within the data set.

So, we can conlude that the two groups are distributed normally and paramateric.

Two variance test find does variances are equal or not:

	Control	Education
Mean	823.8201	1112.757
Variance	61245.34	33855.62
Observations	98	100

Hypothesis test:

df1=n1-1=97

df2=n2-1=99

Significant value= 0.05

Critical value:

The test statistic:

P-value: 0.001812

The test statistic is significant and rejects H0. There is sufficient evidence to conclude that the variances are statistically different.