School Attending and Academic Performance Hypothesis Testing Essay - 1

School Attending and Academic Performance Hypothesis Testing - Essay Example What is the alternative hypothesis? The alternate hypothesis is H0: ÃŽ ¼ = 75.62 (Performance on a test of social skills is same.) What is the null hypothesis? The null hypothesis is Ha: ÃŽ ¼ ≠  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 the 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 (ÃŽ ±) is 0.05, as the Zcrit value of  ± 1.960 refers to 0.05 significance level for a two-tailed test. If a Type I error were made, what would it mean?   Type I error refers to 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 (ÃŽ ²) is about 0.6615. The power (1 – ÃŽ ²) of the test is 0.3385. If a Type II error were made, what would it mean? Type II error refers to 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.