Lmu Is Interested In Student Scholastic Performance The Adm

Lmu Is Interested In Student Scholastic Performance The Administratio

LMU is interested in student scholastic performance. The administration will hire a new advisor to help students learn more effectively. Those in charge wonder if the advisor should initially help men or women. A study was requested to determine the difference in grade point average between the men and women attending LMU. Our MLS270 class was designated as the sample to determine if a true difference existed.

Results will be used to decide who should first receive assistance. Answer the following statements and questions. Use the posted answer form to record your responses to items 1-5.

1. Write the null hypothesis for this study.

2. Write an alternative/research hypothesis for this study.

3. Name the statistical test most appropriate for this study.

4. Should a dependent or independent test be used?

5. How many tails should the test statistic involve?

6. What probability should be used to test for significance? Why?

Answer the missing values in the following table:

Paper For Above instruction

The research question posed by Loyola Marymount University (LMU) aims to investigate whether a significant difference exists in the academic performance, specifically grade point average (GPA), between male and female students. This analysis seeks to inform the decision regarding which group might benefit more initially from targeted academic advising. To evaluate this, a hypothesis test must be conducted comparing the two independent groups—men and women students—using the data gathered from LMU's MLS270 class, serving as the sample.

Formulating the hypotheses is the critical first step. The null hypothesis (H₀) posits that there is no difference in the population means of GPA between male and female students, mathematically expressed as H₀: μ_men = μ_women. Conversely, the alternative hypothesis (H₁) suggests that a difference exists, expressed as H₁: μ_men ≠ μ_women. This bilateral hypothesis allows for the detection of any significant difference, regardless of which group has a higher mean GPA.

The choice of the appropriate statistical test is essential. Given that two independent groups are being compared based on their means, the independent samples t-test (also known as the two-sample t-test) is most fitting. This test assesses whether the means of two independent groups are statistically different from each other, based on sample data, under the assumption of normally distributed data and similar variances.

It is important to distinguish between dependent and independent tests. Since the groups in this study—men and women students—are mutually exclusive and not related or paired observations, an independent samples t-test should be used. Dependent tests, such as paired t-tests, are reserved for related samples, such as pre- and post-test scores for the same subjects.

The number of tails in the test pertains to the hypothesis's nature. Because this study tests whether the means differ significantly in either direction (men's GPA higher or women's GPA higher), a two-tailed test is appropriate. This allows for the detection of differences in both directions and ensures a comprehensive evaluation.

The significance level (α) determines the threshold for rejecting the null hypothesis. Typically, α is set at 0.05 (or 5%), which balances the risk of Type I errors—falsely declaring a difference when none exists. Using a probability of 0.05 ensures that the study's findings are statistically significant if the p-value falls below this level, providing reasonable confidence in the results.

Regarding the missing values, the degrees of freedom (df) for a two-sample t-test are calculated based on the sample sizes of each group. Given that the provided critical value is 4.082 at a certain df and probability, we can reference the t-distribution table. At df = 4, the two-tailed critical value at α = 0.05 is approximately 2.776, whereas at df = 2, it is about 4.303. Since 4.082 lies between these two, it suggests that the degrees of freedom are around 3.

In the provided table, with df = 4.082, the corresponding probability (p) is approximately 0.05, supporting the typical significance threshold. The number of tails is 2, aligning with the two-sided hypothesis, and the critical value associated with this df at α = 0.05 for a two-tailed test is approximately 2.776 — but since the table shows 4.082, it suggests a different significance level or a different approximation. Nonetheless, for standard practice, the critical value at 2 tails and α = 0.05 is around 2.776.

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