Question

In: Statistics and Probability

7. Below are research scenarios. For each, indicate whether the researcher committee a Type 1 error,...

7. Below are 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 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.

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

(c) A researcher found a statistically significant relationship between perceived autonomy and job satisfaction. If the researcher committed an error in hypothesis testing, which error is possible?

Solutions

Expert Solution

(a) In this case there is a strong positive relationship between X and Y, but the researcher failed to capture the relationship and ended up concluding that there is no significant relationship. Here, the researcher fail to reject H0, when H0 is false. So, the researcher committed Type II error.

(b) The researcher found a statistically insignificant difference between group means i.e. he/she failed to reject the null hypothesis H0. But since the researcher has committed an error, then H0 is false. So, it is a Type II error.

(c) The researcher found a statistically significant relationship between perceived autonomy and job satisfaction i.e. he/she rejected the null hypothesis H0. But since, the researcher has committed an error, H0 is true. So, he/she rejected the null hypothesis when it is True. Hence, it is a Type I error.

orchestra answered 2 years ago
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