Question

A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.05 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to​ agree, or is there a substantial​ difference?

Human activity Natural patterns ​Don't know

Male    309    143    59

Female 298 161 60

Identify the null and alternative hypotheses.

Ho​: (1)__________and (2)___________are (3)_____________

H1​: (4)__________and (5)___________are (6)_____________

Compute the test statistic.

_________________________​

(Round to three decimal places as​ needed.)

Find the critical​ value(s).

____________________

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the conclusion based on the hypothesis​ test?

(7)_____________ Ho. There (8)___________sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. Men and women (9)__________to agree.

(1) Respondents who answered yes
   The choice for human activity
   The sex of the respondent
(2) the choice for the cause of global warming
   the respondents who answered no

the choice for natural patterns
(3) independent.
dependent.
(4) Respondents who answered yes
   The choice for human activity
   The sex of the respondent
(5) the respondents who answered no
   the choice for natural patterns
the choice for the cause of global warming
(6) independent.
   dependent.
(7) Reject
   Fail to reject
(8) is not
   is
(9) do not appear
   appear

Answer 1

Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 309 143 59 511 row 2 298 161 60 519 TOTALS 607 304 119 N = 1030 ------------------------------------------------------------------ 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 frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 301.143 150.819 59.038 row 2 305.857 153.181 59.962 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 309 301.143 7.857 61.732 0.205 143 150.819 -7.819 61.137 0.405 59 59.038 -0.038 0.001 0 298 305.857 -7.857 61.732 0.202 161 153.181 7.819 61.137 0.399 60 59.962 0.038 0.001 0 ᴪ^2 o = 1.211 ------------------------------------------------------------------ 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 = 1.211 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| =1.211 & | 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 =0.546 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: 1.211 critical value: 5.991 p-value:0.546 decision: do not reject Ho

we do not have enough evidence to support the claim that  the sex of the respondent is independent of the choice for the cause of global warming. Men and women