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 0.01 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 312 143 50 Female 303 148 54 Click here to view the chi-square distribution table. LOADING... Identify the null and alternative hypotheses. Upper H 0​: ▼ The sex of the respondent Respondents who answered yes The choice for human activity and ▼ the choice for natural patterns the choice for the cause of global warming the respondents who answered no are ▼ dependent. independent. Upper H 1​: ▼ The sex of the respondent The choice for human activity Respondents who answered yes and ▼ the respondents who answered no the choice for natural patterns the choice for the cause of global warming are ▼ independent. dependent. Compute the test statistic. nothing ​(Round to three decimal places as​ needed.) Find the critical​ value(s). nothing ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.) What is the conclusion based on the hypothesis​ test? ▼ Reject Fail to reject Upper H 0. There ▼ is is not 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 ▼ do not appear appear to agree. Enter your answer in each of the answer boxes.

Answer 1

Null Hypothesis

Ho: sex and choice for the cause of global warming are independent

Alternate hypothesis

Ha: sex and choice for the cause of global  warming are dependent

Applying chi square test:

Observed	Oi	human activity	natural pattern	Do not know	Total
	male	312	143	50	505
	female	303	148	54	505
	Total	615	291	104	1010
Expected	Ei=(row*column)/Total	human activity	natural pattern	Do not know	Total
	male	307.5	145.5	52	505
	female	307.5	145.5	52	517
	Total	615	291	104	1010
Chi square	=(Oi-Ei)2/Ei	human activity	natural pattern	Do not know	Total
	male	0.065854	0.042955	0.076923	0.185732
	female	0.065854	0.042955	0.076923	0.185732
	Total	0.131707	0.085911	0.153846	0.371464

Chi square stat is given by below formula

Here degree of freedom is given by below formula

D.f=(Row-1)(Column-1)=(3-1)*(2-1)=2

So for 2 degree of freedom and 0.01 significance level

Chi square Critical value at 0.01 significance level is given as 9.21

Value of chi square stat is given as 0.37

and value of p would be 0.83

It means it is greater than level of significance

Or We fail to reject the null hypothesis

There is not sufficient evidence to support the null hypothesis

Because chi square stat<Chi square critical

Or We fail to reject the null hypothesis

There is not 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 do not appear to agree

hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming