Asked by Allison Bartley on May 29, 2024
Verified
A die,suspected of being unfair,was rolled 50 times.The number of times each face appeared was recorded in the following table. Face Count 18210394115567\begin{array} { c | c } \text { Face } & \text { Count } \\\hline 1 & 8 \\2 & 10 \\3 & 9 \\4 & 11 \\5 & 5 \\6 & 7\end{array} Face 123456 Count 81091157
A) Homogeneity
B) Goodness-of-fit
C) Independence
Unfair Die
A dice that has been modified or weighted in some way to favor certain outcomes over others.
Rolled
Commonly refers to the action of moving or shaping something into a cylindrical or spherical form.
- Outline the variations between chi-square tests of independence, goodness-of-fit, and homogeneity.
- Identify the correct test based on given data and research question.
Verified Answer
SS
Sachin SainiJun 04, 2024
Final Answer :
B
Explanation :
The table shows the observed frequencies of each face, and we can compare these with the expected frequencies if the die was fair. Since there are six faces and 50 rolls, we expect each face to appear 50/6 = 8.33 times on average. A goodness-of-fit test can be used to determine if the observed frequencies differ significantly from the expected frequencies. The null hypothesis is that the die is fair, and we can use a chi-squared test to calculate the test statistic and p-value. If the p-value is less than the significance level (e.g., 0.05), we would reject the null hypothesis and conclude that the die is unfair. Therefore, B is the best choice for this scenario.
Learning Objectives
- Outline the variations between chi-square tests of independence, goodness-of-fit, and homogeneity.
- Identify the correct test based on given data and research question.
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