Use the Following Information to Answer the Question -Carry Out the Randomization Test

question 5

Multiple Choice

Use the following information to answer the question. Math self-efficacy can be defined as one's belief in his or her own
ability to perform mathematical tasks. A college math professor wishes to find out if her students' math self-efficacy matches
reality. To do this she gives a math quiz then asks her students to rate their level of confidence in how well they did on the
quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than
those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling
distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume
that all conditions for a randomization test have been satisfied. $$\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 78.6 & 77.5 & 5.5 & 9.5 \\\hline \text { Low Conf. } & 211 & 73.2 & 72.5 & 4.2 & 8.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. } - \text { Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$$

-Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?

• A) Reject \( \mathrm{H}_{0} \). The professor should conclude that typical quiz scores for those with high confidence is greater than that of those with low confidence. The student's self-efficacy matches reality.
• B) Fail to reject \( \mathrm{H}_{0} \). The professor should conclude that typical quiz scores for those with high confidence is greater than that of those with low confidence. The student's self-efficacy matches reality.
• C) Fail to reject \( \mathrm{H}_{0} \). The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self-efficacy does not match reality.
• D) Reject \( \mathrm{H}_{0} \). The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self-efficacy does not match reality.

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