Save & End Certify Lesson: 10.6 Chi-Square Test for Goodness... O NZINGHA WHITLO

Question

Save & End Certify Lesson: 10.6 Chi-Square Test for Goodness... O NZINGHA WHITLOW 5/30 correct Question 1 of 3, Step 6 of 10 A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. C the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey? Attitude 1st Survey 2nd Survey 8% 8 % 33 % 51% 4% 11% 34% 51% Optimistic slightly Optimistic | slightly pessimistic | Pessimistic Copy Data Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places Submit Ans © 2017 Hawkes Learning : to search

Explanation / Answer

Given table data is as below MATRIX col1 col2 TOTALS row 1 8% 4% 12% row 2 8% 11% 19% row 3 33% 34% 67% row 4 51% 51% 102% TOTALS 100% 100% 200% ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N row 3 row3*col1/N row3*col2/N row 4 row4*col1/N row4*col2/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 6 6 row 2 9.5 9.5 row 3 33.5 33.5 row 4 51 51 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 8 6 2 4 0.667 4 6 -2 4 0.667 8 9.5 -1.5 2.25 0.237 11 9.5 1.5 2.25 0.237 33 33.5 -0.5 0.25 0.007 34 33.5 0.5 0.25 0.007 51 51 0 0 0 51 51 0 0 0 ^2 o = 1.822 ------------------------------------------------------------------ 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 =7.815 since our test is right tailed,reject Ho when ^2 o > 7.815 we use test statistic ^2 o = (Oi-Ei)^2/Ei from the table , ^2 o = 1.822 critical value the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 2 - 1 ) = 3 * 1 = 3 is 7.815 we got | ^2| =1.822 & | ^2 | =7.815 make decision hence value of | ^2 o | < | ^2 | and here we do not reject Ho ^2 p_value =0.61 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: 1.822 critical value: 7.815 p-value:0.61 decision: do not reject Ho

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