A health psychologist wants to determine whether children who eat breakfast perf

Question

A health psychologist wants to determine whether children who eat breakfast perform better on school work than children who do not have a breakfast meal. She gathers two groups for her comparison, 15 children who have a normal breakfast meal and another 15 who do not have breakfast, on a day when they have a math test scheduled in the mid-morning at school. The psychologist plans to use scores on the math test as an indicator of school performance. Respond to the prompts below. . What statistical test would be appropriate in this case? Explain the rationale for your answer. b. Identify the independent variable in this study. c. Identify the dependent variable in this study. d. Describe a potentially confounding variable and explain how that might affect the conclusions from the study. e. State the null and alternative hypotheses in words.

Explanation / Answer

Part (a) :

We are interested in comparing population means of two groups: 1. Children who eat breakfast; 2. Children who do not eat breakfast.   2-sample independent t-test will be appropriate in this case because the two samples of children are independent samples and the sample size 15 is small. Therefore, the test statistic to be used for estimation of difference in population means will follow a t-distribution.

Part (b) :

Independent variable is the Breakfast status (breakfast Taken or breakfast not taken) of the child.

Part (c):

Dependent variable is the Performance in school work measured by child's score on math test.

Part (d) :

A potentially confounding variable is the IQ level of the children being divided into 2 groups. If the grouping is done in such a way that the group who is given breakfast also happens to be that group of children in class who are having very high IQ levels, then the conclusion from the test is confounded by IQ level because higher math score of the group that was given breakfast cannot be fully attributed to the breakfast status. It may be the case that the group that was given breakfast is already high IQ group and hence, their high math score may not be due to taking the breakfast alone.

Part (e) :

Null Hypo: Both groups (with breakfast and without breakfast) have equal population mean for math score.

Alternate Hypo : Group that was given the breakfast has higher mean value for math score than the group without breakfast.

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