Question

Scenario 3: t-test Analysis

Paired Samples Statistics
	Mean	N	Std. Deviation	Std. Error Mean
Pair 1	T1 Scale of student's mathematics utility	-.0096	16021	.99040	.00782
	T2 Scale of student's mathematics utility	.0059	16021	1.00682	.00795

Paired Samples Correlations
	N	Correlation	Sig.
Pair 1	T1 Scale of student's mathematics utility & T2 Scale of student's mathematics utility	16021	.285	.000

Paired Samples Test
	Paired Differences	t	df	Sig. (2-tailed)
	Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
				Lower			Upper
Pair 1	T1 Scale of student's mathematics utility - T2 Scale of student's mathematics utility	-.01556	1.19384	.00943	-.03404	.00293	-1.649	16020	.099

SCENARIO: As an educational researcher, would like to know whether high school student’s perceptions about mathematical utility changed between their freshman and senior year. Each respondent is asked the same series of questions about the utility of mathematics in their future during their freshman and senior year. These questions are combined to form one variable of mathematical utility; higher values indicate higher levels of mathematical utility. Using the High School Longitudinal Survey, please provide: a 1–2 APA style paragraph statement that furnishes an answer to this question, note the relevant statistics, comment on meaningfulness, and include your relevant SPSS output.

QUESTION: We would like to know whether high school student’s perceptions about mathematical utility changed between their freshman and senior year.

Null Hypothesis: High school student’s perceptions about mathematical utility changed between their freshman and senior year.

Alternate Hypothesis: High school student’s perceptions about mathematical utility changed between their freshman and senior year.

In this, we would like to track the same respondent during their freshman and senior year. That means the 2 responses, one in freshman year and the other in senior year are dependent or paired. This allows us to track if the perception of a respondent has changed between the freshman and senior year. Hence this is a Paired sample t-test (The test for the difference between two related variables).

Answer 1