School Attending and Academic Performance Hypothesis Testing - Essay Example

Hypothesis TestingA researcher asks whether attending a private high school leads to higher or lower performance on a test of social skills when compared to students attending public schools. A sample of 100 students from a private school produces a mean score of 71.30. The population mean (μ) for students from public high schools is 75.62. The population standard deviation is 28. Zobt is –1.54. Zcrit is ± 1.96. Should the researcher use a one-tailed or a two-tailed test? Why?The researcher should use a two-tailed test.

This is because the test does not involve any direction. It asks whether there is a difference (higher or lower) in performance on a test of social skills between students attending a private school and students attending public schools.What is the alternative hypothesis?The alternate hypothesis isH0: μ = 75.62 (Performance on a test of social skills is same.)What is the null hypothesis?The null hypothesis isHa: μ ≠ 75.62 (Performance on a test of social skills is different.)What should the researcher conclude about this relationship in the population?

The researcher should conclude that attending a private high school does not lead to higher or lower performance on a test of social skills when compared to students attending public schools.Are the results significant? Explain your response.The results are not significant. The Zobt value of 1.54 falls within non-rejection region (-1.960 to 1.960), thus the null hypothesis H0 is not rejected.What is the probability of making a Type I error? The probability of making a Type I error (α) is 0.05, as the Zcrit value of ± 1.

960 refers for 0.05 significance level for a two-tailed test.If a Type I error were made, what would it mean? Type I error refers for rejecting the null hypothesis when it is in fact true. Thus, if a Type I error were made, it would mean that attending a private high school leads to higher or lower performance on a test of social skills when compared to students attending public schools when in fact it is not true.What is the probability of making a Type II error?The probability of making a Type II error (β) is about 0.6615. The power (1 – β) of the test is 0.3385.If a Type II error were made, what would it mean?

Type II error refers for not rejecting the null hypothesis when it is in fact false. Thus, if a Type II error were made, it would mean that attending a private high school does not lead to higher or lower performance on a test of social skills when compared to students attending public schools when in fact it is false.Appendix 1: Power CalculationStep 1: The left-tail and right-tail critical values for the sample mean are = 70.13, 81.11Reject H0: µ = 75.62 if < 70.13 or > 81.11. Otherwise, do not reject H0.

Step 2: The difference between the critical value and the true mean µ (= ) as a z-value: and Step 3: Find the β risk and power as areas under the normal curvePower = 1 – β = 1 – 0.6615 = 0.3385