The Following Data Represent the Scores of a Sample of 50

question 8

Essay

The following data represent the scores of a sample of 50 randomly chosen students on a standardized test. $$\begin{array} { l l l l l l l l l l } 39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99\end{array}$$ a. Write a 95% confidence interval for the mean score of all students who took the test. b. Identify the target parameter and the point estimator.

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Definitions:

Coefficient Of Determination

A measure used in statistical analysis to assess the goodness of fit of a model, represented as the proportion of variance in the dependent variable that is predictable from the independent variable(s).

Pearson Correlation Coefficient

A measure of the linear correlation between two variables X and Y, giving a value between -1 and 1 which indicates the strength and direction of the correlation.

Sum Of Squares

A statistical measure that quantifies the variation within a set of numbers, calculated as the sum of the squared differences from the mean.

Least Squares Estimates

The estimates of the parameters in a regression model obtained by minimizing the sum of squared differences between observed and predicted values.