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

question 55

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 female students' math self-efficacy
matches reality. To do this she gives a math quiz to the female students then asks them 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. $\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 77.2 & 75.5 & 6.5 & 10.5 \\\hline \text { Low Conf. } & 211 & 62.2 & 59.2 & 5.9 & 9.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. } - \text { Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$

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

• A) 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.
• B) 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.
• C) Fail to reject \( \mathrm{H}_{0} \). The professor should conclude that typical quiz scores for those with high confidence is less than that of those with low confidence. The student's self-efficacy matches reality.
• D) 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.

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