Question

Standar error A police officer would like to estimate the proportion of petty theft cases that have gone unsolved in a large city. He takes a random sample of 72 petty theft cases and finds 45 of these have gone unsolved. Set up the equation for the 90% confidence interval for p.
Estimate x Crit. value x standard error

Answer 1

Answer:

0.625± 1.645*0.0571

Step-by-step explanation:

First calculate the estimate as 72 petty cases and 45 are unsolved as follows :

estimate :72/45=0.625

the critical value is given by cumulative probability equal to the  p* (critical probability) as ,

1)compute value for alpha =1-(confidence value /100).

                                           =1-(90/100)=0.1

for critical probability as p*=1 - (alpha/2)=1 -(0.1/2)=0.95

for this critical value is denoted to central area ,

Z(alpha)=1.645

now the standard error :

s=$\sqrt{\frac{p*q}{n} }$    here p is estimate and q is probability of failure and n is total no of          cases                  

 s=$\sqrt{\frac{0.625*375}{72} }$  =0.0571.