A study is being conducted to determine whether there is a relationship between
ID: 3320985 • Letter: A
Question
A study is being conducted to determine whether there is a relationship between jogging and blood pressure. A random sample of 210 subjects is selected, and they are classified as shown in the table. At alpha 0.05, test the claim that jogging and blood pressure are not related. The numbers without the parenthesis are the observed blood pressures and the number in parenthesis in each cell are the expected blood pressures. Blood Pressure Jogging status Low Moderate High Joggers 34 (26.1) 57 (64) 21 Non joggers 15 (22.9) 63 20 (19.1) State the Ho and Ha hypothesisExplanation / Answer
Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 34 57 21 112 row 2 15 63 20 98 TOTALS 49 120 41 N = 210 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 26.133 64 21.867 row 2 22.867 56 19.133 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 34 26.133 7.867 61.89 2.368 57 64 -7 49 0.766 21 21.867 -0.867 0.752 0.034 15 22.867 -7.867 61.89 2.707 63 56 7 49 0.875 20 19.133 0.867 0.752 0.039 ^2 o = 6.789 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, = 0.05 from standard normal table, chi square value at right tailed, ^2 /2 =5.991 since our test is right tailed,reject Ho when ^2 o > 5.991 we use test statistic ^2 o = (Oi-Ei)^2/Ei from the table , ^2 o = 6.789 critical value the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991 we got | ^2| =6.789 & | ^2 | =5.991 make decision hence value of | ^2 o | > | ^2 | and here we reject Ho ^2 p_value =0.034 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 6.789 critical value: 5.991 p-value:0.034 decision: reject Ho
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