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 ⋮ Determine the significance level for the hypothesis test. ‖ ‖ step 2 ⋮ Compare the p-value from the chi-square test to the significance level. ‖ ‖ step 3 ⋮ Draw a conclusion based on the comparison between the p-value and the significance level. ‖ ***B*** ∻Key Concept∻ ⚹Chi-Square Test for Independence⚹ ∻Explanation∻ ⚹If the p-value is greater than the significance level, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest a relationship between the variables.◊What is the formula for calculating the chi-square statistic in a hypothesis test for independence between two categorical variables?⍭ Generate me a similar question◊⚹

Sia