Perform the Indicated Goodness-Of-Fit Test Do the Data Provide Sufficient Evidence to Conclude That the Hypotheses

question 49

Essay

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
-You roll a die 48 times with the following results. $$\begin{array} { c | r | r | r | r | r | r } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Frequency } & 3 & 12 & 3 & 3 & 14 & 13 \end{array}$$ Do the data provide sufficient evidence to conclude that the die is loaded (i.e., that the six numbers are not equally likely)? Perform the hypothesis test at the 0.05 level of significance.

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Definitions:

Polarization

In psychology, the process by which an individual's opinions or attitudes become more extreme, often influenced by group dynamics.

Cautious Decisions

Decisions made with careful consideration of potential risks and consequences to minimize the likelihood of adverse outcomes.

Group Polarization

Group polarization describes the phenomenon where a group's prevailing attitudes or beliefs become more extreme after group discussions or interactions.

Bystander Effect

This refers to the social psychology concept where the presence of bystanders reduces the probability of someone stepping forward to aid a person in need.