Unit Summary 

Review for the Statistical Techniques We Have Learned
We have learned many different formula and techniques to analyze different types of problems in this course. It is easier to know what technique to apply when we are only talking about certain topics. In real life and in the final exam, we don't have that hint and it is most important to know when to use what statistical technique. The following summary table for statistical techniques provides a review for the subjects we have learned in this course. It is also a good reference when you work on the next section  to choose the statistical techniques for the given problem.
Summary Table for Statistical Techniques
Summary Table for Statistical Techniques 

Inference 
Parameter 
Statistic 
Type of Data 
Examples 
Analysis 
Minitab Command 
Conditions 

1  Estimating a Mean  One Population Mean

Sample Mean 
Numerical  What is the average weight of adults? What is the average cholesterol level of adult females? 
1sample tinterval 
Stat > Basic statistics > 1sample t  data approximately normal OR have a large sample size (n 30) 
2  Test About a Mean  One population Mean

Sample Mean 
Numerical  Is the average GPA of juniors at Penn State higher than 3.0? Is the average winter temperature in State College less than 42°F? 
H_{o}: = H_{a}: The 1sample ttest: 
Stat > Basic statistics > 1sample t  data approximately normal OR have a large sample size (n 30) 
3  Estimating a Proportion  One Population Proportion

Sample Proportion

Categorical (Binary)  What is the proportion of males in the world? What is the proportion of students that smoke? 
1proportion Zinterval 
Stat > Basic statistics > 1sample proportion  have at least 5 in each category 
4  Test About a Proportion  One Population Proportion

Sample Proportion  Categorical (Binary)  Is the proportion of females different from 0.5? Is the proportion of students who fail STAT 500 less than 0.1? 
H_{o}: = _{o} H_{a}: _{o
}OR The one proportion Ztest:

Stat > Basic statistics > 1sample proportion  n_{o} 5 and n (1  _{o}) 5 
5  Estimating the Difference of Two Means  Difference in two population means  
Difference in two sample means  
Numerical  How different are the mean GPAs of males and females? How many fewer colds do vitamin C takers get, on average, than nonvitamin takers? 
2sample tinterval 
Stat > Basic statistics > 2sample t  Independent samples from the two populations Data in each sample are about normal or large samples 
6  Test to Compare Two Means  Difference in two population means  
Difference in two sample means  
Numerical  Do the mean pulse rates of exercisers and nonexercisers differ? Is the mean EDS score for dropouts greater than the mean EDS score for graduates? 
H_{o}: = The 2sample ttest: 
Stat > Basic statistics > 2sample t  Independent samples from the two populations Data in each sample are about normal or large samples 
7  Estimating a Mean with Paired Data  Mean of paired difference 
Sample mean of difference

Numerical  What is the difference in pulse rates, on the average, before and after exercise? 
paired tinterval 
Stat > Basic statistics > Paired t  Differences approximately normal OR Have a large number of pairs (n 30) 
8  Test About a Mean with Paired Data  Mean of paired difference 
Sample mean of difference

Numerical  Is the difference in IQ of pairs of twins zero? Are the pulse rates of people higher after exercise? 
H_{o}: = 0 
Stat > Basic statistics > Paired t  Differences approximately normal OR Have a large number of pairs (n 30) 
9  Estimating the Difference of Two Proportions  Difference in two population proportions _{1}  _{2} 
Difference in two sample proportions _{1}  _{2} 
Categorical (Binary)  How different are the percentages of male and female smokers? How different are the percentages of upper and lowerclass binge drinkers? 
twoproportions Zinterval 
Stat > Basic statistics > 2 proportions  Independent samples from the two populations Have at least 5 in each category for both populations 
10  Test to Compare Two Proportions  Difference in two population proportions _{1}  _{2} 
Difference in two sample proportions _{1}  _{2} 
Categorical (Binary)  Is the percentage of males with lung cancer higher than the percentage of females with lung cancer? Are the percentages of upper and lower class binge drinkers different? 
H_{o}: _{1} = _{2}
The two proportion z test: 
Stat > Basic statistics > 2 proportions  Independent samples from the two populations Have at least 5 in each category for both populations 
11  Relationship in a 2Way Table  Relationship between two categorical variables or difference in two or more population proportions  The observed counts in a twoway table  Categorical  Is there a relationship between smoking and lung cancer? Do the proportions of students in each class who smoke differ? 
H_{o}: The two variables are not related H_{a}: The two variables are related The chisquare statistic: 
Stat > Tables > Chi square Test  All expected counts should be greater than 1 At least 80% of the cells should have an expected count greater than 5 
12  Test About a Slope  Slope of the population regression line 
Sample estimate of the slope b_{1} 
Numerical  Is there a linear relationship between height and weight of a person? 
H_{o}: = 0 H_{a}: 0 OR H_{a}: > 0 OR H_{a}: < 0 The ttest with n  2 degrees of freedom: 
Stat > Regression > Regression  The form of the equation that links the two variables must be correct The error terms are normally distributed The errors terms have equal variances The error terms are independent of each other 
13  Test to Compare Several Means  Population means of the t populations , , ... , 
Sample means of the t populations x_{1}, x_{2}, ... , x_{t} 
Numerical  Is there a difference between the mean GPA of freshman, sophomore, junior, and senior classes? 
H_{o}: = = ... = H_{a}: not all the means are equal The Ftest for oneway ANOVA: 
Stat > ANOVA > Oneway  Each population is normally distributed Independent samples from the t populations Equal population standard deviations 
14  Test to Compare Two Population Variances  Population variances of 2 populations _{1}^{2}, _{2}^{2} 
Sample variances of 2 populations s_{1}^{2}, s_{2}^{2} 
Numerical  Are the variances of length of lumber produced by Company A different from those produced by Company B 
H_{o}: _{1}^{2} = _{2}^{2} H_{a}: _{1}^{2} _{2}^{2} 
Stat > ANOVA > Test of homogeneity  Each population is normally distributed Independent samples from the 2 populations 