Question: Below are several research scenarios. For each, indicate whether the researcher committee a Type 1 error, a Type 2 error, or no error in hypothesis testing .

(a) Assume there is a strong, positive relationship between variable X (number of 6th grade students in a teacher’s classroom) and variable Y (amount of stress that 6th grade teachers experience during the school day) in the population of 6th grade teachers in the United States. That is, the more 6th grade students in the classroom, the more stress the teacher experiences. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 6th grade teachers from local counties. After collecting relevant data, the researcher finds a strong, positive relationship between X and Y and therefore rejects the null hypothesis. The local researcher infers there is a positive relationship between X and Y in the population of 6th grade teachers in the United States.

(b) Assume there is a strong, positive relationship between variable X (number of hours per week a child reads for pleasure) and variable Y (language arts scores in the classroom) in the population of 3rd grade students in the United States. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 3rd grade students from Bulloch County. After collecting relevant data, the researcher finds no relationship between X and Y and therefore fails to rejects the null hypothesis. The local researcher infers there is no relationship between X and Y in the population of 3rd grade students in the United States.

(c) Assume there is no relationship between variable X (number of 6th grade students in a teacher’s classroom) and variable Y (amount of stress that 6th grade teachers experience during the school day) in the population of 6th grade teachers in the United States. That is, the number of 6th grade students in the classroom does not influence the level of stress a teacher experiences. As with any educational study, researchers investigating the relationship between X and Y are not aware of the true relationship in the population, so researchers must conduct studies with samples and then use inferential statistics to make decisions whether to reject the null hypothesis (Ho: There is no relationship between X and Y) or fail to reject the null hypothesis. A local researcher wishes to study the relationship between X and Y and he samples 6th grade teachers from local counties. After collecting relevant data, the researcher finds no relationship between X and Y and therefore fails to reject the null hypothesis (i.e., the researcher states that he believes the null hypothesis is correct). The local researcher infers that X and Y are unrelated in the population of 6th grade teachers in the United States.

(d) A researcher found a statistically significant difference between group means. If the researcher committed an error in hypothesis testing, which error is possible?