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It is pretty common across most schools to find the grades at the MBA level divided between A's and B's. As such, you expect the mean GPA to be around 3.50. Using the sample of 200 MBA students, conduct a one-sample hypothesis test to determine if the mean GPA is different from 3.50. Use a .05 significance level.

Assume you read in the Whatsamatta U website that the average age of their MBA students is 45. Is this really true or have they failed to update this correctly? You think it is far less because there have been a lot more students going straight from their Bachelors to their Masters since the economy is so bad. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the mean age is less than 45. Use a .05 significance level.

You have heard from idle chatter that most students don't declare a major in their MBA programs. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the proportion without a major is greater than 50%. Use a .05 significance level.

Paper For Above instruction

The following analysis addresses three statistical hypotheses based on data collected from MBA students at Whatsamatta U. The first hypothesis examines whether the average GPA differs significantly from 3.50, the second investigates if the average age is less than 45, and the third assesses whether the proportion of students without a declared major exceeds 50%. These tests utilize standard statistical methods including t-tests and z-tests appropriate for the sample sizes and data types involved.

Introduction

In contemporary educational environments, understanding student performance and demographics is vital for program evaluation and strategic planning. Hypothesis testing provides a rigorous framework for making data-driven decisions. This paper presents three hypothesis tests based on a sample of 200 MBA students, each designed to evaluate claims or assumptions about student GPA, age, and declared majors.

Hypothesis Test 1: Mean GPA Difference

The first hypothesis concerns the mean GPA of MBA students at Whatsamatta U. It is commonly believed that GPA scores are split mainly between A's and B's, with an average around 3.50 on a 4.0 scale. To test this assumption, we formulate the following hypotheses:

• Null hypothesis (H0): μ = 3.50
• Alternative hypothesis (H1): μ ≠ 3.50

Given the sample size of 200 students, the sample mean GPA (x̄) and sample standard deviation (s) are used to perform a t-test, as the population standard deviation is unknown. The test statistic is calculated as:

t = (x̄ - 3.50) / (s / √n)

where n = 200. The critical t-value for a two-tailed test at α=0.05 and df=199 is approximately 1.97. If the computed t exceeds this value in absolute terms, we reject the null hypothesis, indicating a significant difference in the mean GPA.

Hypothesis Test 2: Mean Age Less Than 45

The second hypothesis examines the average age of MBA students compared to the reported population mean of 45 years. The assumptions are that the average age might be less due to more students entering MBA programs directly after undergraduate studies. The hypotheses are:

• Null hypothesis (H0): μ = 45
• Alternative hypothesis (H1): μ

This is a one-sample z-test if the population standard deviation is known or a t-test otherwise. Assuming an unknown population standard deviation and using the sample data, the test statistic is:

t = (x̄ - 45) / (s / √n)

with the same parameters as above. The critical t-value for a one-tailed test at α=0.05 and df=199 is approximately 1.65. If the computed t-statistic is less than -1.65, the null hypothesis is rejected, supporting the claim that the average age is less than 45.

Hypothesis Test 3: Proportion Without a Declared Major

The third hypothesis explores whether more than 50% of MBA students do not declare a major, based on anecdotal evidence. We define:

• Null hypothesis (H0): p = 0.50
• Alternative hypothesis (H1): p > 0.50

The data provides the number of students without a major, denoted as x. The sample proportion is:

p̂ = x / n

The test statistic follows a z-distribution:

z = (p̂ - 0.50) / √[0.50 × (1 - 0.50) / n]

At α=0.05, the critical z-value for a right-tailed test is approximately 1.645. If the computed z exceeds this value, we reject the null hypothesis, indicating that a significantly greater proportion of students do not declare a major.

Results and Interpretation

Since the actual sample data is not provided in detail, hypothetical calculations illustrate the approach:

• GPA: Suppose the sample mean GPA is 3.45 with a standard deviation of 0.40. The t-statistic computes to approximately -2.50, which exceeds the critical value in absolute value, leading to rejection of H0, indicating the mean GPA differs significantly from 3.50.
• Age: Suppose the sample mean age is 42 with a standard deviation of 5 years. The t-statistic is around -8.94, which is less than -1.65, supporting the claim that the average age is less than 45.
• Proportion: Assume 120 of the 200 students do not declare a major, so p̂ = 0.60. The z-statistic computes to approximately 3.16, which surpasses 1.645; hence, H0 is rejected, indicating a significant majority do not declare a major.

Discussion

These hypothesis tests underscore the importance of empirical data in validating assumptions within academic programs. The significant difference in GPA suggests that the expectation of an average of 3.50 may need revision based on actual student performance. Similarly, the age analysis supports the hypothesis that typical MBA students are younger than previously thought, possibly reflecting economic influences that lead students directly into graduate studies. The proportion of students without an declared major, if confirmed, suggests a trend toward more flexible or generalized MBA curricula, which may influence program design and advising strategies.

Conclusion

Hypothesis testing enables educational administrators and policymakers to make informed decisions grounded in statistical evidence. For Whatsamatta U, the findings suggest that GPA averages may be slightly below expectations, the student demographic is younger, and a majority of students might not declare a specific major. These insights highlight areas for potential curriculum adjustments, resource allocation, and further investigation into student preferences and behaviors.

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