# Was there a significant difference in the performance of stocks on the tduring the previous year?Уear?6.One hundred army recruits were randomly assigned to four drill sergeantAt the end of boot camp 84 recruits remained, and their performance in theras timed. For Sergeant Adams, 11 of his 20 recruits performed above tSergeant Baker, 8 of her 22 recruits performed above the median. Sergeamn8 of his 20, and Sergeant Davis had 15 perform above the median. Is thedifference in the performance results for the four drill sergeants?ROBLEMS1Show that if a equals b, then Equation 1 becomes Equatiorn 3.2.Show that Equation 1 is the same as Equation 4.2.11 when r equals 2.The usual parametric test for the design in this section (the one-way layoueach observation has a normal distribution instead of being merely a zero oron whether it is below or above the median. If the observations in each sa3.Os when they are below the grand median and 1s if they are equal to or almedian, the statistic for the previous parametric test, computed on the 0s and2(N- c)wn'jj-1 niF =9MAXG(c - 1)j-1 njShow that F may be written as the following function of T,T(N-c)F =(N-T(c- 1)and that therefore rejecting Ho for large T is equivalent to rejecting Ho forMEASURES OF DEPENDENCEThe contingency table is a convenient form for examining data to s609some sort of dependence inherent in the data. The particular type of Po Pulations2SampleTotalsgrand>MedianОтO12arandSMedianO21O22O2cbTotalsn2NncLet a equal the total number of observations above the grand median in allsamples and let b equal the total number of values less than or equal to the grandmedian. Then a b = N, the total number of observations.Assumptions1. Each sample is a random sample.2. The samples are independent of each other.3, The measurement scale is at least ordinal.4, If all populations have the same median, all populations have the sameprobability p of an observation exceeding the grand median.Test Statistic The test statistic is obtained by a rearrangement of the test statisticgiven in the previous section, noting that O ni- Oi in the special case oftwo rows.niaОliN2T =ab(1)i-1booIf a calculator is being used, the following form is more convenient.bO1 Na(2)T =abbniIf a is approximately equal to b, as it should be unless there are many valuesequal to the grand median, the following simplification of the test statistic maybe used.(3)T= (O-O2)2nii 1The simplified form for T given in Equation 3 is exact if a b. It is only approxi-mate otherwise.

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Question 1, equation 1 and equation 3 are in the second image.

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Step 1

To prove equation 1 is equal to equation 2.

If a=b in the following equation.

Step 2

From the table, we understood that...

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