The Scores on a Standardized Test Are Reported by the Testing

question 83

Essay

The scores on a standardized test are reported by the testing agency to have a mean of 70.
Based on his personal observations, a school guidance counselor believes the mean score is
much higher. He collects the following scores from a sample of 50 randomly chosen
students who took the test. $\begin{array} { l l l l l l l l l l } 39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\ 71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\ 79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\ 85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\ 90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99 \end{array}$
Use the data to conduct a test of hypotheses at $\alpha = .05$ to determine whether there is any evidence to support the counselor's suspicions.

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Definitions:

Collectively Exhaustive

A term used to describe a set of events that covers all possible outcomes of an experiment.

P(A)

The probability of event A occurring in a given sample space, representing the likelihood of a specific outcome.

Collectively Exhaustive

A condition where all possible outcomes or cases are considered together, covering every eventuality.

Probability

A measure of the likelihood of a given event occurring, often expressed as a number between 0 and 1.