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.