Significance Tests for Proportions Presentation 9.2

Significance Test for p You can produce a confidence interval for a proportion p. Hypothesis tests can also be performed with one proportion to obtain evidence about the truth about a population.

Hypothesis Test Formulas Null Hypothesis Alternate Hypothesis Test Statistic Remember that p 0 is the null hypothesis and p-hat is the sample proportion. In the standard error formula, we now use p 0 (NOT p-hat) because our calculations are based upon the null hypothesis being true!

M&Ms Example The Mars Company claims that 14% of all plain candies are yellow. A sample from a king size bag found that 9 out of 72 candies were yellow. Is this significant evidence that the true proportion of yellows is not 14%?

M&Ms Example Conduct a 1–proportion z-test. Check assumptions: –The population is greater than 10(n)=10(56)=560 so we may use the standard error formula. –Check np>10 which is 72(.14)>10 and n(1-p)>10 which is 72(.86)>10. Since we pass these, we can approximate with the normal distribution. Then write hypotheses: –The proportion should be.14 (according to the company) –We suspect it may be different.

M&Ms Example Conduct calculations. Test Statistic: –Be sure to use p o in the standard error formula. Then calculate p: –Shown here using the standardized data.

M&Ms Example Conclusions With such a large p- value, we fail to reject the null. There is not sufficient evidence to suggest that the proportion of yellow m&ms is not 14%.

Significance Tests for Proportions This concludes this presentation.