SOLUTION: In a sample of 88 children selected randomly from on town, it is found that 8 of them suffer from asthma. Find the p-value for a test of the claim that the proportion of children w

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Question 875124: In a sample of 88 children selected randomly from on town, it is found that 8 of them suffer from asthma. Find the p-value for a test of the claim that the proportion of children with asthma is equal to 11%
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The alternative hypothesis is p+%3C%3E+0.11 so this is two tailed test.

Given Info

p = 0.11
phat = 8/88 = 1/11 = 0.0909 (roughly)
n = 88


Test Statistic


z = (phat - p)/(sqrt(p*(1-p)/n))
z = (0.0909 - 0.11)/(sqrt(0.11*(1-0.11)/88))
z = -0.57264221039283
z = -0.57


Now use a table to find the area to the left of z = -0.57


The area to the left of z = -0.57 is 0.2843


Double this to get 2*0.2843 = 0.5686 (remember this is a two tailed test)


The p value is 0.5686


Side Note: this very large p value would result in failing to reject the null hypothesis for many standard significance (alpha) values.