One hundred rats whose mothers were exposed to high levels of tobacco smoke duri

Question

One hundred rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats to make a choice between going left (the wrong direction) or right (the correct direction) at the outset. Seventy went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. Let p be the proportion of rats in this population that would go right when running the maze for the first time.

a) Perform a test on whether the true proportion is less than 80%.

b) In order to estimate the proportion with 95% confidence interval to within 4%, how many size is needed.  

Explanation / Answer

here null hypothesis:Ho p>=0.8

alternate hypothesis: Ha: p<0.8

hence std error =(p(!-p)/n)1/2 =0.04

hence test stat z=(p-0.8)/0.04

if z stat <-1.6448 we reject null hypothesis; and accept that  true proportion is less than 80%

b) here p=0.8

margin of error E =0.04

for 95% CI, z=1.96

hence sample size =p(1-p)(Z/E)2 =~385( rounding it down)

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