108 men are randomly sampled and asked if they would prefer a puppy or a bowling ball as a gift, and 47 chose a puppy.
Find a 95\% confidence interval for the population proportion of men who would prefer a puppy as a gift.
Interpret the meaning of this interval in the context of the problem. Do men appear to prefer bowling balls to puppies? Why or why not?
Find a 95\% confidence interval for the population proportion of men who would prefer a puppy as a gift.
Interpret the meaning of this interval in the context of the problem. Do men appear to prefer bowling balls to puppies? Why or why not?
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If the population proportion of men who prefer pups as a gift is p, then the sample
proportion, ps, has an approximate Normal distribution with mean p and SD sqrt[p(1-p)/108]
Since p is unknown we use ps as an approximation to it so
SD=sqrt[(47/108)(61/108)/108]=0.04771 approx.
The 95% CI for p is given by 47/108 - 1.96(0.04771)
or 0.3417
For men to prefer bowling to puppies requires p < 0.5
The confidence interval can support either p<0.5 or p>0.5 so there is no evidence.
Also a significance test Ho:p=0.5, Ha: p<0.5 would have test statistic ps with mean 0.5
and SD=sqrt[(0.5)(0.5)/108] =0.04811 and Z=(47/108 -0.5)/0.04811=-1.35 which
has a -value 0 0.089 which is not significant at level 0.05
proportion, ps, has an approximate Normal distribution with mean p and SD sqrt[p(1-p)/108]
Since p is unknown we use ps as an approximation to it so
SD=sqrt[(47/108)(61/108)/108]=0.04771 approx.
The 95% CI for p is given by 47/108 - 1.96(0.04771)
The confidence interval can support either p<0.5 or p>0.5 so there is no evidence.
Also a significance test Ho:p=0.5, Ha: p<0.5 would have test statistic ps with mean 0.5
and SD=sqrt[(0.5)(0.5)/108] =0.04811 and Z=(47/108 -0.5)/0.04811=-1.35 which
has a -value 0 0.089 which is not significant at level 0.05
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Men prefer the bowling balls. Multiply 45 by 0.95 for your answer.