The Scores on a Standardized Test Are Reported by the Testing

Essay

The scores on a standardized test are reported by the testing agency to have a mean of 75.
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.

$$\begin{array}{l}\begin{array} { l l l l l l l l l l } 39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99\end{array}\\\\\text { Find and interpret the } p \text {-value for the test of } H _ { 0 } : \mu = 75 \text { against } H _ { \mathrm { a } } : \mu > 75 \text {. }\end{array}$$