Remark

• When doing t distribution problems, you MUST use SPSS.
• For confidence interval, the default option is 95%. You may have to change it when you are doing your homework.

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.