Question

A researcher drew a random sample of 24 people seeking asylum in the United States and recorded whether they were granted amnesty ("yes" or "no"). The researcher also grouped them according to their gender ("male" or "female"). The results are below:

Granted General Amnesty

Gender of Asylum Seeker	Yes	No
Male	5	4
Female	8	7

Enter this information into SPSS. Use this information to answer questions #4 - #7.

Question 4

Identify the null hypothesis and research (alternative) hypothesis.

Group of answer choices

Null Hypothesis

      [ Choose ]            There is no true relationship between gender and amnesty.            There is a true relationship between gender and amnesty.      

Research (Alternative) Hypothesis

      [ Choose ]            There is no true relationship between gender and amnesty.            There is a true relationship between gender and amnesty.      

Question 5

What is the value of chi-square?

Question 6

What is the associated probability?

Question 7

The researcher should retain the null hypothesis.

Group of answer choices

True

False

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 5 4 9 row 2 8 7 15 TOTALS 13 11 N = 24 ------------------------------------------------------------------ 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 4.875 4.125 row 2 8.125 6.875 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 5 4.875 0.125 0.0156 0.0032 4 4.125 -0.125 0.0156 0.0038 8 8.125 -0.125 0.0156 0.0019 7 6.875 0.125 0.0156 0.0023 ᴪ^2 o = 0.0112 ------------------------------------------------------------------ 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 =3.8415 since our test is right tailed,reject Ho when ᴪ^2 o > 3.8415 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 0.0112 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415 we got | ᴪ^2| =0.0112 & | ᴪ^2 α | =3.8415 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.9157 ANSWERS --------------- 4. 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 5. test statistic: 0.0112 critical value: 3.8415 6. p-value:0.9157 decision: do not reject Ho

7. we do not have enough evidence to support the claim that  true relationship between gender and amnesty.

option:B

false