Assignment: Gender and student performance

Assignment: Gender and student performance

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Identify an appropriate research question that would require the use of a z-, t-, or Chi-Square test to answer. Pick the question from the list created in Week 1 or identify a new question if there are no appropriate ones from Week 1.

Research question #7.

Is there any relationship between gender and student performance in statistics and science subjects?

The variables, in this case, will be the average performance of the students in the subjects of focus, they will be categorized according to their gender. These variables can actually be measured using the ratio level of measurements by some mathematical operations. In this case, an average will be calculated of both genders performance on the subjects being studied. The data in this study will depict some continuous characteristics.

Describe why this question is appropriate for the selected statistical test.

Solution

The test to be used in this question is independent T-test. Independent T-test compares the means of two groups that are not related in any way. Performance of males and females are to be investigated to check whether the gender contributes to passing or failing statistics and science subjects. Performance for males is to be compared with the one for females. T- Statics compares their means and tells us whether there males or females perform well in statists and science subjects. Data for performance is continuous. This is a requirement when using t-test.

Identify the variables in this study and each of their attributes: discrete or continuous, quantitative or categorical, the scale of measurement (nominal, ordinal, interval, or ratio), an independent or dependent.

Solution

The variables here are:

Gender – is a categorical variable taking two categories, that is, male or female.

Performance – is a continuous taking real numbers

There is no dependent variable in the case of independent T-test statistics.

Explain how the variables do or do not fit the qualifications for the selected statistical test

Solution

Both variables fit the independent t-test statistics selected. Performance is categorized into two groups, that is, Males and Females. The performance means are then compared in the two groups.

Provide a written explanation for the null and alternative hypotheses.

Solution

The null hypothesis indicated with H0, states that there no relationship between gender and performance. Alternative hypothesis H1, indicates there is a significant mean deference when comparing results for males and females.

This can be written as;

H0: μ1 = μ2 = 0

H1: μ1 ≠ μ2 ≠ 0

Rejecting the null hypothesis will means there is confidence in failing to reject the alternative hypothesis.

Describe the types of errors that could occur.

Solution

Type I error and type II error can occur on the testing hypothesis. Type I error occurs when a true null hypothesis is rejected. Type II error occurs when one fails to reject a false null hypothesis.

In this case, concluding that there is a difference in means while in a real sense there isn’t, is a type I error and concluding there is no difference in means while there is, is a type II error.