Q1. Practice paired observation procedures for the following 6 samples to test if the difference for Company A and Company B is positive.

Background

Topic: Paired t-test for mean difference

This question tests your ability to conduct a paired t-test to determine if the mean difference between two related samples (Company A and Company B) is significantly greater than zero.

Key Terms and Formulas

• Paired t-test: Used when comparing two related groups.

• Mean difference (): Average of the differences between paired observations.

• Standard deviation of differences (): Measures variability of the differences.

• Test statistic:

• Critical value (CV): Value from t-distribution table for given significance level ().

Step-by-Step Guidance

1. Calculate the difference for each pair: for all 6 samples.

2. Find the mean difference: , where is the number of pairs.

3. Compute the standard deviation of the differences: .

4. Set up the null hypothesis: (no difference).

5. Calculate the t-statistic: .

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Q2. The human resources department is studying absenteeism with employees. They have gathered data and want to test if absenteeism is different between two departments using paired observations.

Background

Topic: Paired t-test for mean difference

This question tests your ability to use paired t-tests to compare absenteeism between two departments using matched pairs of employees.

Key Terms and Formulas

• Paired t-test: Used for comparing two related groups.

• Mean difference (), standard deviation (), t-statistic (), and critical value (CV).

• Test statistic:

Step-by-Step Guidance

1. Calculate the difference for each employee: .

2. Compute the mean difference: .

3. Find the standard deviation of differences: .

4. State the null hypothesis: .

5. Calculate the t-statistic: .

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Q3. Below is the output for regression equation for 10 observations with 2 independent variables. Use 4 decimal places for CV. Use two decimal places for interval.

Background

Topic: Linear Regression and Confidence Intervals

This question tests your ability to interpret regression output, write the regression equation, and calculate confidence intervals for regression coefficients.

Key Terms and Formulas

• Regression equation:

• Confidence interval for slope:

• Standard error (SE): Provided in regression output.

• Critical value (CV): From t-distribution for given degrees of freedom.

Step-by-Step Guidance

1. Write the regression equation using the coefficients from the table.

2. Identify the standard error for the slope and the critical value for the confidence interval.

3. Set up the confidence interval formula: .

4. Plug in the values for the slope, critical value, and standard error.

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