Lecture 14 Testing a Hypothesis about Two Independent Means

Independence  No relationship between the people or objects in groups  Book example: People who use the internet daily and those who do not

Choosing a Hypothesis Test  Testing a single mean Comparing the mean health of 20-year olds to the mean of the general population  Population: general population  Test value: mean health of 20-year olds Testing the hypothesis that on average, the work week is 40 hours long  Population: all workers  Test value: 40 hours

Choosing a Hypothesis Test  Testing two independent means Testing the hypothesis that individuals in their 20’s and individuals in their 50’s watch the same amount of TV  People in their 20’s  People in their 50’s

Examples  Hypothesis: The average income of a 20 year old is the same as the average income for all Americans  What is the alternative hypothesis?  What type of test should we use?  What are the important variables?

Examples  Hypothesis: The mean income for 20 year olds and 50 year old in 2004 is the same  What is the alternative hypothesis?  What type of test should we use?  What are the important variables?

Difference Between Sample Means  Test to see if the difference is zero  Difference is normally distributed  Variance decreases as sample size increases

Standard Error of Mean Difference

Computing the T-Statistic Likeliness of an observed difference

SPSS Output

Confidence Interval  95% of the time, the confidence interval will contain the true difference  If the confidence interval contains zero, we cannot say the means are not the same

Variance  2 ways to estimate standard error: Assume variance of the populations is the same Assume variance of the populations is different Levine test determines whether there is a difference between variances If the significance is small, reject the hypothesis that the two variances are equal

Pooled Estimate of Variance

Hypothesis Testing  Ho: There is no differences between means  Ha: There is a difference between means  Conduct a t-test to determine if we can REJECT the null hypothesis

Example  Individuals making between $10,000 and $12,499 have the same number of years of education (educ) on average as individuals making between $40,000 and $49,999.

In-Class Activity  Conduct a hypothesis test to evaluate the following assertions:  Men and women (sex) have the same number of children on average (childs)  Men and women attend school for the same length of time (educ)  Men and women earn the same amount of money on average (rincome06)