Significance Test for the Difference of Two Proportions

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Presentation transcript:

Significance Test for the Difference of Two Proportions Section 8.4 Significance Test for the Difference of Two Proportions

Quiz 8.3 – 8.4 tomorrow 1 side of a note card

Suppose: We have two populations.

Suppose: We have two populations. The proportion of successes for each population is 0.2 so …

Suppose: We have two populations The proportion of successes for each population is 0.2 so p1 = p2

Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions,

Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times

Next, we do this same process for samples of size 50 and 100 Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times Next, we do this same process for samples of size 50 and 100

Next, we do this same process for samples of size 50 and 100 Suppose: We take a pair of samples of size 30 from each population and calculate the difference in their proportions, We repeat this process 5000 times Next, we do this same process for samples of size 50 and 100 Where do we expect the center of the distribution to be?

Where do we expect the center of the distribution to be? 0 because p1 = p2 Recall, the mean of the differences is equal to the difference of the means.

As n1 and n2 increase? Shape: Center: Spread:

As n1 and n2 increase? Shape: more normal Center: Spread:

As n1 and n2 increase? Shape: more normal Center: stays at 0 Spread:

As n1 and n2 increase? Shape: more normal Center: stays at 0 Spread: decreases

Standard Error As n1 and n2 increase, the standard error decreases. To find standard error, use formula: SE =

Standard Error

Page 536, P48

Page 536, P48 (a) After millions of repetitions, we would expect and to both equal 0.12. Thus, the expected value of the difference of would be 0.12 - 0.12 = 0.

Page 536, P48

Page 536, P48

Page 536, P48 d. Using the calculator, normalcdf(.05,1E99, 0, .0154) gives approximately 0.00058. Note: This is not a standard normal distribution so must also use mean and standard error.

Time to go to work on Fathom Lab 8.4a! Due: Wednesday

Questions?