2 sample interval proportions sample Shown with two examples

Always check conditions  Each of the populations must be at least (10) times each of the corresponding sample sizes; and one sample does not influence the other  Random Sample... randomly selected or randomly assigned  Large Sample Size; Normality (the sample has at least 10 expected successes and at least 10 expected failures)  Independence... Population at least 10 times sample size; and each observation has no influence on any other

Pew Survey on Stem Cell Research (found on page 360)  The researchers from the Pew study interviewed two random samples. Both samples, the one taken in 2002 and the one taken in 2009, had 1500 people. In 2002, 645 people expressed support for stem cell research. In 2009, 870 expressed support. These data are summarized in the table below: Total Support Stem Cell Research Do Not Support Total

Using Minitab

Our confidence level will be 95 and we want to find out if they are not equal to.

Results from Minitab  Test and CI for Two Proportions  Sample X N Sample p    Difference = p (1) - p (2)  Estimate for difference:  95% CI for difference: ( , )  Test for difference = 0 (vs not = 0): Z = P-Value = Analysis:  Our main concern is for the P- value in this example it is =  Since this is below our 5% confidence interval we are going to reject the null hypothesis

Don’t forget to properly interpret your findings!  Reject H o. With a p-value of 0.00, and assuming an α = 0.05, we conclude that we do have statistically significant evidence that the proportion stem cell research supporters differs from the national value.

Another example (8.78 found on page 379)  In 2009 a Gallup Poll reported that 40% of people said they have a gun in their home. In the same year, a Pew Poll reported that 33% of people said they have a gun in the home. Assume that each poll used a sample size of  Do these polls disagree? Test the Hypothesis that the two populations proportions are different. Use a significance level of 0.05.

Using Mini tab we will follow the same steps used in the previous example

Don’t forget to set your confidence level and alternative tab accordingly

Results: Test and CI for Two Proportions Sample X N Sample p Difference = p (1) - p (2) Estimate for difference: % CI for difference: ( , ) Test for difference = 0 (vs not = 0): Z = 3.26 P-Value = Interpretation Reject H o. With a p-value of 0.001, and assuming an α = 0.05, we conclude that we do have statistically significant evidence that the proportion of gun owners differs from the national value.