Using The Table Showing The Number Of Students

Using The Table Below Showing The Number Of Students Who Are Taking A

Using the table below showing the number of students who are taking a statistics course in the traditional face-to-face mode versus online by gender. Assume one person is chosen at random from the 165. What is the probability that person is a male student taking the course in the traditional mode? Enter your answer as a fraction (a/b). Online Traditional Totals Male Female Totals .

I am deciding on whether to invest 400,000 CAD to open a convenience store in a particular spot in Ottawa. I know that the business will be profitable, with income of 70,000 CAD per year, if the store will have an average μ = 60 or more customers per day. If I am convinced that the business will be profitable then I will go ahead and open the store otherwise I won’t. Hence I am dealing with this hypothesis testing problem. H0 : μ = 60 vs Ha : μ

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Paper For Above instruction

Introduction

Statistical analysis provides a crucial foundation for decision-making across various fields, including education and business. In this discussion, we analyze two distinct statistical problems: a probability question involving student course enrollment and gender, and a hypothesis testing scenario related to business profitability. By understanding how to calculate probabilities and interpret errors in hypothesis testing, we can make informed decisions rooted in statistical evidence.

Probability of a Male Student in Traditional Mode

The initial problem involves a table (though not explicitly provided here) showing the number of students enrolled in a statistics course in both face-to-face (traditional) and online modes, broken down by gender. The total number of students surveyed is 165. To find the probability that a randomly selected student is a male enrolled in the traditional face-to-face mode, we need the number of male students in traditional mode divided by the total number of students.

Assuming the table provides specific counts:

- Number of male students in traditional mode: \( M_{trad} \)

- Total number of students: 165

The probability is:

\[

P(\text{Male in traditional mode}) = \frac{M_{trad}}{165}

\]

Since the exact numbers are not specified here, the general approach involves identifying \( M_{trad} \) from the data and constructing the fraction. If, for example, 50 male students are enrolled in traditional classes, then:

\[

P = \frac{50}{165}

\]

This calculation allows for a straightforward understanding of the likelihood of randomly selecting a male student in the traditional learning environment.

Hypothesis Testing for Business Profitability

The second problem revolves around determining whether a new convenience store in Ottawa will likely be profitable based on customer traffic, modeled through hypothesis testing. The key parameters involve an income threshold of 70,000 CAD per year, equating to an average daily customer count \( \mu \). The hypotheses are:

- Null hypothesis (\( H_0 \)): \(\mu = 60\)

- Alternative hypothesis (\( H_a \)): \(\mu

This setup suggests that if the true average number of customers per day is less than 60, the business might not be profitable, given the assumed link between customer flow and income.

(A) Explanation of Type I Error:

A Type I error occurs when the hypothesis test incorrectly rejects the null hypothesis (\( H_0: \mu = 60 \)) when it is actually true. In this context, it means concluding that the average daily customers are fewer than 60 (\(\mu

(B) Consequences of Type I Error:

The primary consequence involves missed business opportunity. If the decision-maker erroneously rejects \( H_0 \), they might forego opening a store that would indeed be profitable, resulting in lost revenue and return on investment.

(C) Explanation of Type II Error:

A Type II error occurs when the test fails to reject the null hypothesis (\( H_0: \mu = 60 \)) when the alternative hypothesis is true (\(\mu

(D) Consequences of Type II Error:

The consequence involves a missed opportunity for profit. The business owner might avoid opening a potentially profitable store due to an incorrect failure to reject the null hypothesis, resulting in lost income from the missed market.

(E) Which Error is More Expensive?

In the context of business, the more costly error is generally the Type I error—rejecting \( H_0 \) when it is true—because it results in passing up a profitable opportunity. Deciding not to open the store based on a false conclusion that it wouldn’t be profitable can lead to greater financial loss over time than opening a store that ultimately might not perform as expected. Conversely, the cost of a Type II error, i.e., missing out on a potentially profitable store, while significant, generally involves opportunity costs that can be mitigated with further analysis and data collection. Therefore, in most entrepreneurial contexts, avoiding Type I errors tends to be prioritized due to the higher associated risk of missing out on profitable ventures.

Conclusion

Both problems highlight the importance of understanding probabilistic calculations and statistical hypothesis testing in decision-making. Whether estimating the likelihood of a student’s enrollment characteristics or evaluating the feasibility of a business investment, proper statistical reasoning ensures that decisions are evidence-based and minimize costly errors. Recognizing the nature and implications of Type I and Type II errors is crucial in applying hypothesis testing appropriately, especially in high-stakes scenarios such as business investments.

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