# Lab 6 Chapter 6 and Section 7.1

### STAT 301 Lab Sections

### Wutao Wei

# 1-sided/2-sided test

- Hypothesis: vs
- 1-sided: or
- 2-sided:

# Test statistic

- When you
**know** the standard deviation (**population**), please use z-statistic
- When you
**do not know** the standard deviation (**population**), please use t-statistic

# P-value

- First write down , , or
- If the alternative is 2 sided, they should use the SPSS P-value. If it is 1-sided, they need to draw the curve to decide whether to divide the SPSS P-value by 2 or to divide by 2 and subtract the result from 1.

# Conclusion

- When , we
**reject** null hypothesis;
- then we draw conclusion that
*population parameters*(need to be specific) is greater/less(1-sided) or do not equal to(2-sided) what you are testing.
- If not, we
**cannot reject** null hypothesis;
- then we draw conclusion that there is no enough evidence to show that
*population parameters*(need to be specific) is greater/less(1-sided) or do not equal to(2-sided) what you are testing.
- Never say
*accept* or *prove*. Then draw concusion include the word **population**.

# Robustness Guidelines

- If your sample size is , You can use the t procedures as long as Your data is perfectly symmetric and Normally distributed with no outliers or skewness.
- If your sample size is , You can use the t procedures as long as Your data is fairly symmetric and Normally distributed with no outliers and no heavy skewness.
- If your sample size is , You can use the t procedures as long as Your data is symmetric or skewed, but you should not have any outliers.