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 0.05significance 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 knowMale       313                    133                       52Female  306                     157                      49Identify the null and alternative hypotheses.Compute the test statistic. (round 3 decimal places) Find the critical​ value(s). (round 3 decimal places) What is the conclusion based on the hypothesis​ test?

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Asked Dec 6, 2019
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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       313                    133                       52
Female  306                     157                      49

Identify the null and alternative hypotheses.

Compute the test statistic. (round 3 decimal places)

 

Find the critical​ value(s). (round 3 decimal places)
 
What is the conclusion based on the hypothesis​ test?
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Expert Answer

Step 1

The appropriate null and alternative hypotheses are stated below:

H0: The sex of the respondent and the choice for the cause of global warming are independent.

H1: The sex of the respondent and the choice for the cause of global warming not independent.

From the given information, the level of significance is 0.05.

The number of degrees of freedom is obtained as follows:

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Degrees of freedom = (Rows-1)(Columns –1) = (2-1)(3–1) = 2

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Step 2

Therefore, the number of degrees of freedom is 2.

Step-by-step procedure to find the critical value using MINITAB software:

  • Choose Graph > Probability Distribution Plot > View Probability > OK.
  • From Distribution, choose ‘Chi-Square
  • Enter Degrees of freedom is 2.
  • Click the Shaded Area
  • Choose Probability and Right Tail for the region of the curve to shade.
  • Enter the data value as 05.
  • Click OK.

Output using MINITAB software is obtained as follows:

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Distribution Plot Chi-Square, df =2 a5 04 03 02 0.1- 0.05 0.0 5.991 х Density

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Step 3

From the output, the critical value of chi-square is 5.991.

The general decision rule is reject the null hypothesis if test statistic > critical value.

Therefore, the decision rule is reject the null hypothesis if test statistic > 5.991.

Test statistic:

Step-by-step procedure to find the test statistic using MINITAB software:

  • Choose Stat > Tables > Chi-Square Test for Association.
  • Choose Summarized data in a two-way table.
  • In ...
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Chi-Square Test for Association: Gender, Worksheet columns Rows: Gender Columns: Worksheet columns Natural Human Dont know All activity patterns 313 52 Male 133 498 305.2 143 49.8 306 Female 157 49 512 313.8 147 51.2 619 All 290 101 1010 Cell Contents Count Expected count Chi-Square Test Chi-Square DF P-Value Pearson 1.961 0.375 Likelihood Ratio 1.963 0.375

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