Basketball players can take shots worth 3 points, 2 points, or 1 point. A scout is assessing two players-Tabitha and Lauren-who play for different teams in different leagues. The scout wonders if they have similar or different shot selections. They take a random sample of Tabitha's games and a separate random sample of Lauren's games. They tally how many of each type of shot the players attempted in those games. Here is a summary and the results of a chi-square test:
\begin{tabular}{lrr}
\multicolumn{3}{c}{ Chi-square test: Shot vs. } \
player \
Tabitha
\end{tabular}

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 shot type differs between Tabitha and Lauren.
(B) This isn't enough evidence to say that the distribution of shot type differs between Tabitha and Lauren.
(c) This is convincing evidence that shot type and player are not independent.
(D) They lack evidence to say that shot type and player are not independent.

Question

Basketball players can take shots worth 3 points, 2 points, or 1 point. A scout is assessing two players-Tabitha and Lauren-who play for different teams in different leagues. The scout wonders if they have similar or different shot selections. They take a random sample of Tabitha's games and a separate random sample of Lauren's games. They tally how many of each type of shot the players attempted in those games. Here is a summary and the results of a chi-square test:
\begin{tabular}{lrr}
\multicolumn{3}{c}{ Chi-square test: Shot vs. } \
player \
Tabitha
\end{tabular}

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 shot type differs between Tabitha and Lauren.
(B) This isn't enough evidence to say that the distribution of shot type differs between Tabitha and Lauren.
(c) This is convincing evidence that shot type and player are not independent.
(D) They lack evidence to say that shot type and player are not independent.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the null and alternative hypotheses for the chi-square test. The null hypothesis ($H_0$) is that the distribution of shot types is the same for both players. The alternative hypothesis ($H_a$) is that the distribution of shot types is different for the two players. ‖ ‖ step 2 ⋮ Compare the p-value to the significance level ($\alpha = 0.05$). The p-value given is 0.350. ‖ ‖ step 3 ⋮ Since the p-value (0.350) is greater than the significance level (0.05), we fail to reject the null hypothesis. ‖ ‖ step 4 ⋮ Based on the failure to reject the null hypothesis, we conclude that there is not enough evidence to say that the distribution of shot types differs between Tabitha and Lauren. ‖ ∻Answer∻ ***B*** ∻Key Concept∻ ⚹Chi-square test interpretation⚹ ∻Explanation∻ ⚹If the p-value is greater than the significance level, we fail to reject the null hypothesis, indicating insufficient evidence to support a difference in distributions.⚹◊What is the formula for calculating the expected frequency in a chi-square test for independence?⍭ Generate me a similar question◊

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