Question 984195: A consumer group claims that less than 25% (.25) of all the kindergarteners in Texas favor pancakes as their breakfast food. A survey of 700 kindergarteners in Texas revealed that 160 favor pancakes as their breakfast food. The survey result is to be used to test the claim with 5% (.05) level of significance. Set up the null hypothesis and the alternative hypothesis. Is this a right-tailed or left-tailed test?
Answer by mathmate(429)   (Show Source):
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Given:
Claim: proportion of pancake-lovers less than 0.25
Sample of 700 people netted 160 pancake-eaters.
Test at the 0.95 level the validity of the claim.
Solution:
Define hypotheses:
H0 (null hypothesis) : proportion of pancake-eaters is greater than or equal to 0.25
Ha (alternate hypothesis) : proportion of pancake-eaters is less than 0.25.
Critical Z-score for 95% confidence (left-tail), Zc = -1.645
population proportion, p = 0.25
sample size, n=700,
sample proportion, ps
= 160/700
= 0.2286
sample standard error, sigma_p
= sqrt(p(1-p)/n)
= sqrt(0.25(0.75)/700)
= 0.01637
sample z-score, Zp
= (ps-p)/sigma_p
= ((160/700-0.25)/0.01637)
= -1.309
Since Zp > Zc at 95% confidence level, there is insufficient evidence to reject the null hypothesis H0, hence we conclude that the proportion of pancake eaters is greater than or equal to 25%,
and reject the claim (Ha) that there are less than 25% of pancake eaters.
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