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?
What is the alternative hypothesis?
What is the null hypothesis?
What should the researcher conclude about this relationship in the population?
Are the results significant? Explain your response.
What is the probability of making a Type I error?
If a Type I error were made, what would it mean?
What is the probability of making a Type II error?
If a Type II error were made, what would it mean?
We do not do your work for you. Once you have attempted to answer your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
However, I will give you a start.
If you are considering both higher or lower, would you use a one tailed test?
Ho = mean1 = mean2
Ha = mean 1 ≠ mean2
No
two tailed because we have two directions of interest.
alternative hypothesis is mean is not equal to 75.62.
null hypo is mean is equal to 75.62.
There is evidence that private schools can lead to higher or lower performance on a test of social skills. (type 2 error)
type 2 error = 95%
type 1 error= 5%
if a type 1 error was made then there would be no evidence that private schools can lead higher or lower performance on a test of social skills.
To determine whether the researcher should use a one-tailed or a two-tailed test, we need to consider the directionality of the alternative hypothesis. In this case, the researcher is interested in whether attending a private high school leads to higher or lower performance on the test of social skills compared to public schools. Since there is no specific direction mentioned, the researcher should use a two-tailed test.
The alternative hypothesis (H1) in this case would be that there is a statistically significant difference in social skills performance between students from private and public high schools. In other words, attending a private high school either leads to higher or lower performance on the social skills test compared to attending a public school.
The null hypothesis (H0) would state that there is no significant difference in social skills performance between students from private and public high schools. In other words, attending a private high school does not have an impact on the social skills test scores compared to attending a public school.
Based on the given information, the researcher should conclude that there is no statistically significant relationship between attending a private high school and performance on the social skills test in the population.
The results are not significant in this case because the absolute value of Zobt (–1.54) is less than the absolute value of Zcrit (1.96). This means that the calculated test statistic does not fall within the critical region, indicating that we fail to reject the null hypothesis and do not have enough evidence to support the alternative hypothesis.
The probability of making a Type I error, also known as the significance level (α), is typically predetermined. Although it is not explicitly mentioned in the given information, it is common to set the significance level at α = 0.05, which means there is a 5% chance of making a Type I error.
If a Type I error were made, it would mean that the researcher incorrectly rejects the null hypothesis and concludes that there is a significant difference in social skills performance between students from private and public high schools, when in reality, there is no such difference.
The probability of making a Type II error (β) depends on various factors such as the sample size, effect size, and the chosen significance level. The information provided does not allow us to directly calculate the probability of Type II error, as it requires additional information.
If a Type II error were made, it would mean that the researcher incorrectly fails to reject the null hypothesis and concludes that there is no significant difference in social skills performance between students from private and public high schools, when in fact, there is a true difference.