(a) State the null and alternative hypothesis.
(b) Are the mean rates of return different at the alpha = 0.05 level of significance? Please explain your answer, citing numeric and other evidence in support of your response.
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Make recommendations for the design choice.
Explain whether you think that this is the appropriate t test to use for the question. Why or why not?
As a lay reader, were you able to understand the results and their implications? Why or why not?
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Discussion – Week 6 Attachment

The variable X1SCIID is a scale of the student’s science identity. Students who agree with the statements “You see yourself as a science person” and/or “Others see me as a science person” will have higher values for X1SCIID (High School Longitudinal Study of 2009, n.d.). My research question centers on whether or not the science identity of male students is different from the science identity of female students. This is a cross sectional research design with focus on the variables student’s science identity and student’s sex.

Hypothesis:

H0: Mu1=Mu2

H1: Mu1 is not equal to Mu2

Mu1= mean student science identity of male students

Mu2 = mean student science identity of female students

Statistical Test: 2 sample t-test with independent means. According to Drew, Hardman & Hosp (2008), this parametric analysis is appropriate for interval data such as student’s science identity. In addition, independent means is used since the scores of males are not affected by the scores of females and vise versa and this is not a pre-test/post-test design (which would indicate a paired means model).

Significance level: alpha= .05

In order to use the t-test with independent means, Frankfort-Nachmias and Leon-Guerrero (2015) state that certain assumptions must be met.

Assumptions:

The samples of females and males are independent – In this case the variable student’s science identity is divided into subgroups (male and female) and this satisfies assumption of independence.
The sample is random – This is met as the High School Longitudinal Study (n.d.) states that the sample is random.
The variable X1SCIID is measured at an interval-ratio level of measurement.
N1 = 10036 and N2= 9903 – since both are greater than 50 we can assume the sampling distribution is normal from the empirical rule even though we do not know that the population is normally distributed.
Population variances – with alpha .05, H0: variance of sample 1 = variance of sample 2 and H1 is variance of sample 1 is not equal to variance of sample 2. P-value = .041 based on Levene’s test of equality of variances. Therefore the null hypothesis is rejected and we conclude that the variances are unequal. The t obtained that we will use for this model is the one corresponding to equal variances not assumed.

With the assumptions met, the 2 sample t-test with independent means is calculated (see attached).

Independent variable = student sex; dependent variable = mean student’s science identity score.

With DF = 19918.434, t statistic = 6.309 and p-value = <.001 which exceeds our .05 level of significance, we reject the null hypothesis. Conclusion – At the .05 level of significance, the data provides sufficient evidence that the mean science identity score of male students is not equal to the mean science identity score of female students. References: Drew, C. J., Hardman, M. L., & Hosp, J. L. (2008). Inferential statistics. In Designing and conducting research in education. (pp. 305-335). Thousand Oaks, CA: SAGE Publications, Inc. doi: http://dx.doi.org.ezp.waldenulibrary.org/10.4135/9781483385648.n13 Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.). Thousand Oaks, CA: Sage Publications. High School Logitudinal Study of 2009 (n.d.). Retrieved from http://nces.ed.gov/surveys/hsls09/index.asp