A geneticist was curious about the relationship between gender and dominant hand. They surveyed a random sample of 500 people. Here is a summary of the responses and the results from a chi-squared test:

Chi-square test: Dominant hand vs. gender
\begin{tabular}{lrr}
& Men & Women \
\hline Right & 207 & 227 \
Expected & 208.32 & 225.68 \
Left & 21 & 27 \
Expected & 23.04 & 24.96 \
Ambidextrous & 12 & 6 \
Expected & 8.64 & 9.36
\end{tabular}
$\chi^{2}=2.876, \mathrm{DF}=2, \mathrm{P}$-value $=0.237$
Assume that all conditions for inference were met.
At the $\alpha=0.05$ significance level, what is the most appropriate conclusion to draw from this test?

Choose 1 answer:
(A) This is convincing evidence that the distribution of dominant hand differs between the genders.
(B) This isn't enough evidence to say that the distribution of dominant hand differs between the genders.
(c) This is convincing evidence that dominant hand and gender are not independent.
(D) They lack evidence to say that dominant hand and gender are not independent.
(E) Gender causes people to be more likely to be left- or right-handed.

Question

A geneticist was curious about the relationship between gender and dominant hand. They surveyed a random sample of 500 people. Here is a summary of the responses and the results from a chi-squared test:

Chi-square test: Dominant hand vs. gender
\begin{tabular}{lrr} 
& Men & Women \
\hline Right & 207 & 227 \
Expected & 208.32 & 225.68 \
Left & 21 & 27 \
Expected & 23.04 & 24.96 \
Ambidextrous & 12 & 6 \
Expected & 8.64 & 9.36
\end{tabular}
$\chi^{2}=2.876, \mathrm{DF}=2, \mathrm{P}$-value $=0.237$
Assume that all conditions for inference were met.
At the $\alpha=0.05$ significance level, what is the most appropriate conclusion to draw from this test?

Choose 1 answer:
(A) This is convincing evidence that the distribution of dominant hand differs between the genders.
(B) This isn't enough evidence to say that the distribution of dominant hand differs between the genders.
(c) This is convincing evidence that dominant hand and gender are not independent.
(D) They lack evidence to say that dominant hand and gender are not independent.
(E) Gender causes people to be more likely to be left- or right-handed.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the most appropriate conclusion from the Chi-square test, we compare the p-value to the significance level $\alpha$. ‖ ‖ step 2 ⋮ The p-value is 0.237, which is greater than the significance level $\alpha = 0.05$. ‖ ‖ step 3 ⋮ If the p-value is greater than $\alpha$, we fail to reject the null hypothesis. ‖ ‖ step 4 ⋮ The null hypothesis in the context of a Chi-square test for independence is that there is no association between the two categorical variables—in this case, dominant hand and gender. ‖ ‖ step 5 ⋮ Since we fail to reject the null hypothesis, there is not enough evidence to conclude that there is an association between dominant hand and gender. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Chi-square test for independence⚹ ∻Explanation∻ ⚹When the p-value is greater than the significance level, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the alternative hypothesis of an association between the variables.⚹◊What is the formula for calculating the Chi-square test statistic in this context?⍭ Generate me a similar question◊

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