posted by Shawna on .
A 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 (m) 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?
In this study the researcher will use a two-tailed test. Two-tailed tests look for an effect in either direction. Therefore, they have two-tailed probabilities. A two-tailed test is when you predict that there is a relationship but you do not predict what the outcome will be but rather let it fall as it may. When the researcher started his study, he wanted to know if performance was higher or lower. He did not mention that he thought it would be either or. Therefore, because he did not predict what he thought the outcome would be, you would use a two-tailed test.
• What is the alternative hypothesis?
An alternative hypothesis describes the population parameters that the sample data represent if the predicted relationship does exist. Therefore, I believe that the alternative hypothesis would be that the scores from the private school would not equal the population mean for students in public schools and vice versa.
• What is the null hypothesis?
A null hypothesis describes the population parameters that the sample data represent if the predicted relationship does not exist. Therefore, our null hypothesis would indicate that there is no significant difference between the results at the public school and the private school.
• What should the researcher conclude about this relationship in the population?
• Are the results significant? Explain your response.
I believe that the results were not significant. Non-significant indicates the differences reflected by the results were likely to have occurred through chance or sampling error; without there being a relationship in nature. Therefore, I believe the results occurred through chance because if those same students or different students took the performance test, the results would be very different. If the same students took the test a second time, their results would be either better or worse than they were before. If different students took the test, their results would be either roughly around the same as the other’s or they would be higher or lower.
• What is the probability of making a Type I error?
In some cases, there may have been some students who scored above 1.96 or below -1.96, even though the distributions could be identical. In a normal circumstance this should happen 5% of the time. Therefore, there is a 5% chance of rejecting the hypothesis that is in fact true.
• If a Type I error were made, what would it mean?
A Type I error is rejecting the null hypothesis when it is true. In other words, it is saying that the independent variable is working when it really doesn’t.
• What is the probability of making a Type II error?
• If a Type II error were made, what would it mean?
A Type II error is retaining the null hypothesis when it is false. In other words, we fail to identify the independent variable that really does work. The reason for this is because the sample represents the relationship that is present poorly. Therefore, the statistics are fooled into concluding that the relationship is not present.
I just want to see if I am on the right track and if so please let me know...if not can you please help me out... thank you so much
It all looks good!