Question

3.Problem 3

The Business Graduate School at RUM is studying the test scores from this year's candidates. In particular, we are interested to know if the there is a dependent relationship between the candidates' verbal and quantitative scores.  

		Quantitative Scores
		Low	High
Verbal Scores	Low	39	155
	High	22	170

Use an alpha = 0.025.

What is the critical value for this test?

Select one:

a. 11.14

b. 7.38

c. 3.84

d. 5.02

I just need the answer

Answer 1

3.

Given table data is as below MATRIX col1 col2 TOTALS row 1 39 155 194 row 2 22 170 192 TOTALS 61 325 N = 386 ------------------------------------------------------------------ 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 ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 30.66 163.34 row 2 30.34 161.66 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 39 30.66 8.34 69.56 2.27 155 163.34 -8.34 69.56 0.43 22 30.34 -8.34 69.56 2.29 170 161.66 8.34 69.56 0.43 ᴪ^2 o = 5.42 ------------------------------------------------------------------ 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 = 0.025 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =5.02 since our test is right tailed,reject Ho when ᴪ^2 o > 5.02 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 5.42 critical value the value of |ᴪ^2 α| at los 0.025 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 5.02 we got | ᴪ^2| =5.42 & | ᴪ^2 α | =5.02 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0.02 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: 5.42 critical value: 5.02 option:D p-value:0.02 decision: reject Ho

we have enough evidence to support the claim that  if the there is a dependent relationship between the candidates' verbal and quantitative scores.