Question 1197977
**a) Choose the correct set of hypotheses for a two-tailed test for a zero slope.**

* **H0: β1 = 0 vs. H1: β1 ≠ 0** 

This set of hypotheses correctly represents a two-tailed test for a zero slope. 

* H0: β1 = 0 (null hypothesis): The slope of the regression line is zero, meaning there is no linear relationship between the number of operators (X) and the wait time (Y).
* H1: β1 ≠ 0 (alternative hypothesis): The slope of the regression line is not zero, meaning there is a linear relationship between the number of operators (X) and the wait time (Y).

**b-1) What is the p-value?**

To find the p-value, you would typically use statistical software like Excel, R, or Python. 

* **In Excel:**
    1. **Data Analysis Toolpak:** Ensure the Data Analysis Toolpak is enabled in Excel (File -> Options -> Add-ins -> Excel Add-ins -> Go -> Check "Analysis Toolpak").
    2. **Data Analysis:** Go to "Data" -> "Data Analysis" -> "Regression".
    3. **Input:** 
        * Input Y Range: Select the "Wait Time (Y)" column.
        * Input X Range: Select the "Operators (X)" column.
        * Check "Labels" if you have included column headers.
    4. **Output Options:** Choose an output location.
    5. **Click "OK".**

The regression output will include the p-value for the slope coefficient. 

* **Note:** Since the sample size is very small (n = 5), the results of the regression analysis might not be very reliable.

**b-2) State the 95% confidence interval for the slope.**

The 95% confidence interval for the slope will also be provided in the regression output from Excel. It will be presented in the form:

* **Slope ± Margin of Error**

**c) Choose the correct statement.**

* **To determine the correct statement, you need to compare the p-value to your chosen significance level (usually 0.05).**

    * If p-value ≤ 0.05: Reject the null hypothesis (H0). The slope is significantly different from zero. 
    * If p-value > 0.05: Fail to reject the null hypothesis (H0). The slope is not significantly different from zero.

**Disclaimer:** 

* I cannot provide the exact p-value or confidence interval without the actual Excel output. 
* With a sample size of only 5, the results of the regression analysis may not be statistically significant. 

I hope this helps! Let me know if you have any further questions.