Analysis of Regional Interest in an Online Accounting Course

QUESTION

Question 9

A US-based internet company offers an online proficiency course in basic accounting. Completing this online course satisfies the “fundamental of accounting” course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal intrest in the course across all regions. Test at 10% significance. What do you find to be true.

1. The critical statistic is 10.644.
2. Do not reject the null hypothesis.
3. The denominator in the formula would be 52
4. The test statistic is 12.5916

5. ANSWER

 Analysis of Regional Interest in an Online Accounting Course

Introduction

In the era of digital education, online courses have gained immense popularity for their convenience and accessibility. A US-based internet company is offering an online proficiency course in basic accounting, which satisfies the “fundamentals of accounting” course requirement in many MBA programs. To gauge the regional interest in the course, the marketing research manager has divided the country into seven regions of approximately equal population and collected enrollment data for each region.

Data Analysis

The data shows the course enrollment values for each of the seven regions, with the following information:

Region Enrollment
1 45
2 60
3 30
4 40
5 50
6 55
7 35

Hypothesis Testing

The management wants to determine whether there is equal interest in the course across all regions. To address this, a hypothesis test is performed at a significance level of 10%. The null hypothesis (H0) assumes that there is no difference in interest across the regions, while the alternative hypothesis (Ha) suggests that there is a significant difference.

The test statistic for hypothesis testing is calculated using the formula:

\[ t = \frac{\bar{x} – \mu}{\frac{s}{\sqrt{n}}} \]

Where:
– \( \bar{x} \) is the sample mean,
– \( \mu \) is the population mean (assuming equal interest across regions),
– \( s \) is the sample standard deviation,
– \( n \) is the sample size (number of regions).

With the given data, the sample mean \( \bar{x} \) is calculated as:

\[ \bar{x} = \frac{45 + 60 + 30 + 40 + 50 + 55 + 35}{7} = \frac{315}{7} ≈ 45 \]

The sample standard deviation \( s \) can be calculated using the formula:

\[ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i – \bar{x})^2} \]

where \( x_i \) represents the individual enrollment values for each region. The calculated \( s \) is approximately 10.22.

As there are 7 regions, \( n = 7 \).

The population mean \( \mu \) is the overall mean enrollment, which can be calculated as:

\[ \mu = \frac{\sum_{i=1}^{n}x_i}{n} = \frac{315}{7} ≈ 45 \]

With the above information, we can calculate the test statistic:

\[ t = \frac{45 – 45}{\frac{10.22}{\sqrt{7}}} \approx 0 \]

Conclusion

The calculated test statistic is approximately 0. Given the critical statistic of 10.644 and the significance level of 10%, we do not reject the null hypothesis. This means that there is no significant evidence to suggest unequal interest in the online accounting course across the seven regions.

In summary, based on the hypothesis test, we find that there is no significant difference in the interest for the online proficiency course in basic accounting across the seven regions. The marketing research manager can confidently conclude that the course has a consistent appeal to students in different parts of the country, which bodes well for its acceptance as a fundamental accounting course in MBA programs.