I am faced with the following question:

The proportion of US smokers $(p_1) = 136/157$.

The proportion of Non-US smokers $(p_2) = 21/157$.

To test $H_0 : p_1 = p_2$ versus $H_1 : p_1 > p_2$ at 5% significance, the data provides evidence to reject NULL hypothesis by using the value of ?

$(a)\quad Z \quad (b)\quad \chi^2 \quad (c)\quad \text{Both }Z\text{ and }\chi^2 \quad (d)\quad \text{Neither}$.

I obtained the $\chi^2$ value as $15.10$ and $Z$ value as $3.887$ (which I can see is the square root of $\chi^2$). There are multiple questions in the paper with similar options. My guess is that since chi-square test is more appropriate for independence between variables a $Z$ test should be used here.

  • 1
    $\begingroup$ Take a close look at the alternative here. $\endgroup$
    – Glen_b
    Dec 27, 2019 at 7:59
  • $\begingroup$ Use MathJax for typesetting math. And please add the self-study tag. $\endgroup$ Dec 27, 2019 at 8:08
  • $\begingroup$ @Glen_b-ReinstateMonica Thanks, I get it now. $\endgroup$
    – Dom Jo
    Dec 27, 2019 at 8:27


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