Question

1. Assume that a father of a teenager in the US is concerned about the number of crimes in schools that involve guns. After some investigation, he finds out that out of 320 crime reports in schools, 210 of the crimes involve a gun.

   1. Estimate with 90% confidence the proportion of crimes in schools that involve a gun.

   2. How many reports would this father need to find in order to be within 1 percentage point, with 95% confidence?

Answer 1

given data and some necessary calculations are :-

sample size (n) = 320

sample proportion () = 210/320 = 0.65625

a).z critical value for 90% confidence level, both tailed test be:-

the 90% confidence interval be:-

we are 90 % confident that the true proportion of crimes in schools that involve a gun will be within 0.613 and 0.700

b).given data are:-

margin of error (E) = 1 % =0.01

p = 0.65625 [ i am using the sample proportion calculated in the previous part ]

z critical value for 95% confidence level, both tailed test be:-

the needed sample size be:-

this father need to find 8667 reports.

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