The researchers continue their chi-square independence test, by finding a critical value and making a conclusion about the null hypothesis. (The contingency table below shows the observed frequencies above th expected frequencies.) Table Reads: StartLayout 1st Row 1st Column Blank 2nd Column Bold Yes 3rd Column Bold No 4th Column Bold Row Total 2nd Row 1st Column Bold 17 to 24 Years 2nd Column 37 Bold 26.5 3rd Column 18 Bold 28.5 4th Column 55 3rd Row 1st Column Bold 25 to 35 Bold Years 2nd Column 30 Bold 26.5 3rd Column 25 Bold 28.5 4th Column 55 4th Row 1st Column Bold 36 to 50 Years 2nd Column 15 Bold 26.5 3rd Column 40 Bold 28.5 4th Column 55 5th Row 1st Column Bold 50 plus Years 2nd Column 24 Bold 26.5 3rd Column 31 Bold 38.5 4th Column 55 6th Row 1st Column Bold Column Total 2nd Column 106 3rd Column 114 4th Column 220 EndLayout. H0: The two variables are independent, so age does not affect desire to ride a bicycle. Ha: The two variables are dependent, so age does affect desire to ride a bicycle. α=0.01. The test statistic, χ20=19.01. Use this portion of the χ2-Table to find the critical value: df...345678χ20.10...6.2517.7799.23610.64512.01713.362χ20.05...7.8159.48811.07012.59214.06715.507χ20.025...9.34811.14312.83314.44916.01317.535χ20.01...11.34513.27715.08616.81218.47520.090χ20.005...12.83814.86016.75018.54820.27821.955 Which is the correct conclusion of the researchers' independence test, at the 1% significance level? Select the correct answer below: Degrees of freedom = (r−1)(c−1)=3 Critical value: χ20.01=11.345 Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should reject H0 because the test statistic falls into the rejection region. Interpretation: At the 1% significance level, the data provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are dependent. Degrees of freedom = (r−1)(c−1)=3 Critical value: χ20.01=11.345 Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should NOT reject H0 because the test statistic does NOT fall into the rejection region. Interpretation: At the 1% significance level, the data does NOT provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are independent. Degrees of freedom = (r)(c)=8 Critical value: χ20.01=20.090 Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should reject H0 because the test statistic falls into the rejection region. Interpretation: At the 1% significance level, the data provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are dependent. Degrees of freedom = (r)(c)=8 Critical value: χ20.01=20.090 Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should NOT reject H0 because the test statistic does NOT fall into the rejection region. Interpretation: At the 1% significance level, the data does NOT provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are independent.
The researchers continue their chi-square independence test, by finding a critical value and making a conclusion about the null hypothesis. (The
Table Reads: StartLayout 1st Row 1st Column Blank 2nd Column Bold Yes 3rd Column Bold No 4th Column Bold Row Total 2nd Row 1st Column Bold 17 to 24 Years 2nd Column 37 Bold 26.5 3rd Column 18 Bold 28.5 4th Column 55 3rd Row 1st Column Bold 25 to 35 Bold Years 2nd Column 30 Bold 26.5 3rd Column 25 Bold 28.5 4th Column 55 4th Row 1st Column Bold 36 to 50 Years 2nd Column 15 Bold 26.5 3rd Column 40 Bold 28.5 4th Column 55 5th Row 1st Column Bold 50 plus Years 2nd Column 24 Bold 26.5 3rd Column 31 Bold 38.5 4th Column 55 6th Row 1st Column Bold Column Total 2nd Column 106 3rd Column 114 4th Column 220 EndLayout.
- H0: The two variables are independent, so age does not affect desire to ride a bicycle.
Ha: The two variables are dependent, so age does affect desire to ride a bicycle. - α=0.01.
- The test statistic, χ20=19.01.
Use this portion of the χ2-Table to find the critical value:
Select the correct answer below:
Degrees of freedom = (r−1)(c−1)=3
Critical value: χ20.01=11.345
Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should reject H0 because the test statistic falls into the rejection region.
Interpretation: At the 1% significance level, the data provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are dependent.
Degrees of freedom = (r−1)(c−1)=3
Critical value: χ20.01=11.345
Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should NOT reject H0 because the test statistic does NOT fall into the rejection region.
Interpretation: At the 1% significance level, the data does NOT provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are independent.
Degrees of freedom = (r)(c)=8
Critical value: χ20.01=20.090
Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should reject H0 because the test statistic falls into the rejection region.
Interpretation: At the 1% significance level, the data provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are dependent.
Degrees of freedom = (r)(c)=8
Critical value: χ20.01=20.090
Conclusion: The test statistic is greater than the critical value (χ20>χ20.01). So, we should NOT reject H0 because the test statistic does NOT fall into the rejection region.
Interpretation: At the 1% significance level, the data does NOT provides sufficient evidence to conclude that age does affect a person's desire to ride a bicycle. So, we can assume the variables are independent.
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