7.4 Hypothesis Testing for Proportions
• Key Concepts:
– Sample Proportion vs Population Proportion
– Sampling Distribution of the Sample
Proportion
– The z-test for a Population Proportion p
7.4 Hypothesis Testing for Proportions
• We built confidence intervals for a population
proportion p in chapter 6.
– We used the sampling distribution of sample
proportions to build the interval:
p  p
p 
pq
n
p is approximately normal provided n p  5 and nq  5
7.4 Hypothesis Testing for Proportions
• How can we use this information?
– Since we know the sample proportions are normally
distributed and we’re assuming the null hypothesis is
true, we can standardize p-hat as follows:
z
p  po
po 1  po 
n
where po is the hypothesized population proportion
7.4 Hypothesis Testing for Proportions
• Since our test statistic follows the standard
normal distribution, we can use the p-value or
the critical-value approach in these tests.
– Guidelines are given on page 388.
#12 p. 391 (Asthma)
#16 p. 392 (Cat Ownership)