Statistics Homework Solutions 153

Statistics Homework Solutions 153 - 153 SECTION 6.9 The...

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Unformatted text preview: 153 SECTION 6.9 The signed ranks are Signed Rank 2 2 2 4 55 55 7 8 9 10 x0 0 01 0 01 0 01 0 03 0 05 0 05 0 07 0 11 0 13 0 15 ¨ ¨ ¨ ¨ ¨ ¡ ¨ ¡ ¨ ¨ ¨ x 0 01 0 01 0 01 0 03 0 05 0 05 0 07 0 11 0 13 0 15 ¡ ¨ ¨ ¨ ¡ ¨ ¡ ¡ ¨ ¡ ¨ ¡ ¡ ¨ ¡ ¨ ¡ ¡ ¨ ¨ ¡ 5. ¨ ¡ ¨ ¡ ¡ ¨ 23 5. n 0. 10. ¡ ¡ ¨ ¢ ¡ The sum of the positive signed ranks is S 0 versus H1 : µ ¡ The null and alternate hypotheses are H0 : µ Since the alternate hypothesis is of the form µ µ0 , the P-value is twice the area under the signed rank probability mass function corresponding to S 23 5. ¡ ¨ ¢ ¨ 0 2324. ¡¥ 2 0 1162 ¨ ¨ ¡ ¤ From the signed-rank table, P We cannot conclude that the gauges differ. The ranks of the combined samples are Value Rank Sample 12 1 X 13 2 X 15 3 X 18 4 Y 19 5 X 20 6 X 21 7 X 23 8 Y 24 9 Y 27 10 X 30 11 Y 32 12 Y 35 13 Y 40 14 Y ¡ µY 0 versus H1 : µX ¡ ¡ The null and alternate hypotheses are H0 : µX µY ¡ 0. The test statistic W is the sum of the ranks corresponding to the X sample. 7 and n ¡ 34. The sample sizes are m 7. ¡ ¡ W Since the alternate hypothesis is of the form µX µY probability mass function corresponding to W 34. ¡ ¨ ¡¥ 2 0 0087 0 0174. ¨ ¨ ¤ ¡ From the rank-sum table, P We can conclude that the mean recovery times differ. ¡ 7. ∆, the P-value is twice the area under the rank-sum ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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