Question: An achievement test is said to be reliable if a
An achievement test is said to be reliable if a student who takes the test several times will consistently get high (or low) scores. One way of checking the reliability of a test is to divide it into two parts, usually the even-numbered problems and the odd- numbered problems, and observe the correlation between the scores that students get in both halves of the test. Thus, the following data represent the grades, x and y, that 20 students obtained for the even- numbered problems and the odd- numbered problems of a new objective test designed to test eighth grade achievement in general science:
Calculate r for these data and test its significance, that is, the null hypothesis ρ = 0 against the alternative hypothesis ρ ≠ 0 at the 0.05 level of significance.
Answer to relevant QuestionsWith reference to Exercise 14.65, use the formula obtained in Exercise 14.31 to construct a 95% confidence interval for ρ. In Exercise Formula The calculation of r can often be simplified by adding the same constant to each x, adding the same constant to each y, or multiplying each x and/or y by the same positive constants. Recalculate r for the data of Example ...The following are sample data provided by a moving company on the weights of six shipments, the distances they were moved, and the damage that was incurred: (a) Assuming that the regression is linear, estimate β0, β1, and ...(a) Fit a linear surface to the following data: (b) How good a fit is obtained? (c) Plot the residuals against and determine whether the pattern is “random.” (d) Check for multicollinearity among the independent ...The following are the numbers of mistakes made in five successive weeks by four technicians working for a medical laboratory: Test at the 0.05 level of significance whether the differences among the four sample means can be ...
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