Question

O Assignment Score: 80% Resources Ds Give Up? Give Up O Hint Question 3 of 5 Check Answer Check Answer Attempt 10 - Does artistic ability determine which type of operating system a person prefers? Suppose that a market research company randomly selected = 259 adults who used a desktop or laptop outside of the workplace (tablets and smartphones were excluded). The subjects were asked to identify the operating system of the desktop or laptop they used the most. The operating systems were classified as Windows, Mac OS, and Linux. There were no other operating systems reported in the survey. The subjects were administered a test for creative imagery ability (TCIA), and based on the results, were classified as being exceptionally artistic or not. Exceptionally artistic was defined as being above the third quartile (the top 25 percent) of all people who took the TCIA. The table contains the results of the study. Windows Mac OS Linux Total Exceptional 464 3 53 Not exceptional 182 14 10 206 Total 228 18 13 259 If you wish, you may download the data in your preferred format. Crunchit! CSV Excel JMP Mac Text Minitab PC Text RSPSS TI Cale preference are dependent. Their null hypothesis is that they are independent. Assuming that artistic ability and operating system preference are independent, compute the expected number. E. of subjects who would prefer the Windows operating system and are rated as not exceptional in terms of artistic ability Give your answer precise to two decimal places.

the answer is not 2.66

Answer 1

3.

Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 46 4 3 53 row 2 182 14 10 206 TOTALS 228 18 13 N = 259 ------------------------------------------------------------------ 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 46.656 3.683 2.66 row 2 181.344 14.317 10.34 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 46 46.656 -0.656 0.43 0.009 4 3.683 0.317 0.1 0.027 3 2.66 0.34 0.116 0.044 182 181.344 0.656 0.43 0.002 14 14.317 -0.317 0.1 0.007 10 10.34 -0.34 0.116 0.011 ᴪ^2 o = 0.1 ------------------------------------------------------------------ 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, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =5.991 since our test is right tailed,reject Ho when ᴪ^2 o > 5.991 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 0.1 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991 we got | ᴪ^2| =0.1 & | ᴪ^2 α | =5.991 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.951 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: 0.1 critical value: 5.991 p-value:0.951 decision: do not reject Ho

we do not have enough evidence to support the claim that there is a association of artistic ability and operating system are independent