**Unformatted text preview: **t' 2
was In" Suppose a random sample of size n = 1000 yields 260 successes. Partially “men The sample proportion is 13: 0.26 v 7.00 points out of 8.00 A normal distribution is a good approximation for the sampling distribution of proportions if up 2 10 and 110 - 13) Z 10.
‘7 Flag question In this example up = 260 ~/ and n(1 -j5).= 740 v . When it is appropriate to approximate the distribution of sample proportions with a normal distribution. a good approximation for the standard error
(SE) for the distribution of sample proportions is given by the formula 130—13)
n . In this example the formula yields SE: 0.014 w/ . When it is appropriate to approximate the distribution of sample proportions with a normal distribution. a confidence interval for the population
proportion can be computed with the formula
Era—:3) c as
piz " . where z“ is the standard normal endpoint for the desired level of confidence. In this example, a 95% confidence interval is 0.23 V to 0.29 V . When it is appropriate to approximate the distribution of sample proportions with a normal distribution, we can test Ho : p 2 p0 vs H“ : p ;E 170 (or
a two-tail alternative) using the standardized test statistic _ IB—Po
Z _ SE where SE is given by the formula ‘ I Faun—P“) . computed using the null proportion p0 In this example, to use our sample proportion to test the null hypothesis H0 2 p = 0.2, we get test statistic z = 0.46 X with corresponding one—tailed p—value of 0.0002 v . ...

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