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To solve this hypothesis testing problem in Excel, follow these steps:

### Hypothesis:
The problem is to test whether there is a significant difference between the average performance (marks) of engineering (coded as "2") and non-engineering (coded as "1") students.

We can conduct an **independent two-sample t-test** for this:

- **Null Hypothesis (H₀):** The mean marks of engineering students (Group 2) is equal to the mean marks of non-engineering students (Group 1). \( \mu_1 = \mu_2 \)
- **Alternative Hypothesis (H₁):** The mean marks of engineering students (Group 2) is different from the mean marks of non-engineering students (Group 1). \( \mu_1 \neq \mu_2 \)

### Steps in Excel:

1. **Input the Data:**
   - Column A: Serial Number (1 to 30)
   - Column B: Marks
   - Column C: UG (1 = Non Engineer, 2 = Engineer)

2. **Separate the Data:**
   - Filter the data based on the "UG" column.
   - Create two groups:
     - Group 1 (Non-engineers, UG = 1)
     - Group 2 (Engineers, UG = 2)

3. **Calculate Descriptive Statistics for Each Group:**
   - Use `=AVERAGE(range)` to calculate the mean for each group.
   - Use `=STDEV.P(range)` or `=STDEV.S(range)` to calculate the standard deviation.
   - Count the number of students in each group with `=COUNT(range)`.

4. **Perform the Two-Sample t-Test:**
   - Use Excel's built-in **T-Test** function:
     - Go to the "Data" tab → "Data Analysis" → "t-Test: Two-Sample Assuming Equal Variances" (or Unequal Variances if justified).
     - Input the ranges for the two groups.
     - Set the alpha level (usually 0.05 for a 95% confidence level).
     - Excel will give the test statistic (t-statistic) and the **p-value**.

### Expected Output:

1. **Means** for both groups.
2. **t-statistic** and **p-value** from the t-test.
3. **Conclusion** based on the p-value:
   - If \( p \leq \alpha \) (typically 0.05), reject the null hypothesis (there is a significant difference between the two groups).
   - If \( p > \alpha \), fail to reject the null hypothesis (no significant difference between the two groups).

Would you like me to perform the t-test calculations, or would you like further guidance on how to set this up? 

### 5 Follow-up Questions:
1. What is the importance of choosing between equal and unequal variance in a t-test?
2. How does sample size affect the outcome of a t-test?
3. Can we use other tests like the ANOVA for this case? Why or why not?
4. What does the p-value represent in the context of hypothesis testing?
5. How would the result change if we used a one-tailed test instead of a two-tailed test?

### Tip:
When performing a t-test in Excel, always make sure to double-check whether equal or unequal variances apply, as it influences the calculation of the t-statistic.

Test if the average performance of students from engineering stream is the same as that of non-engineers.

Test whether there is a significant difference between the average performance of engineering and non-engineering students using an independent two-sample t-test. Learn how to conduct the test using Excel, covering hypothesis formulation, descriptive statistics, and interpreting the t-test results.

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