Question

2) A researcher develops a test for selecting intellectually gifted children, with a µ of 56 and a σx of 8. Using this test, you measure 64 children, obtaining a X of 57.28. Your friend says that because this X is so close to the µ of 56, this sample could hardly be considered gifted. Perform the appropriate statistical procedure to determine whether he is correct.

Answer 1

We need to conduct the One-sample, Right-tail test for dfference of mean, when population standard deviation is known. We choose the right tail, because the objective for gifted children to have a higher score than the population mean. Let us choose the significance level of 0.05 to conduct the test

Conclusion: Observed statistic does not fall in the critical range, i.e. 1.28 is less than the critical value 1.645. Hence, we fail to reject the null hypothesis and conclude that the chosen sample is not of intellectually gifted children