A survey asked During the last year did anyone take somethin

A survey asked, \"During the last year, did anyone take something from you by using force such as a stickup, mugging, or threat?\" Of 994 subjects, 17 answered yes and 977 answered no. a. Find the point estimate of the proportion of the population who were victims. p = (Round to five decimal places as needed.) b. Find the standard error of this estimate. se = (Round to five decimal places as needed.) c. Find the margin of error for a 95% confidence interval. (Round to five decimal places as needed.) d. Construct the 95% confidence interval for the population proportion. ( , ) (Round to five decimal places as needed.) Can you conclude that fewer than 10% of all adults were victims? A. No, more than 10% of all adults were victims. B. Yes, fewer than 10% of all adults were victims. C. No conclusion can be drawn by using the 95% confidence interval.

Solution

A survey asked, \"During the last year, did anyone take something from you by using force such as a stickup, mugging, or threat?\" Of 994 subjects, 17 answered yes and 977 answered no.

a. the point estimate of the proportion of the population who were victims=number of persons who answered yes/total number of persons=17/994=0.01710 [answer]

b. the standard error of the estimate is se=sqrt[0.01710*(1-0.01710)/994]=0.00411 [answer]

c. since here sample size=n=994 is very large the assumption is that the distribution of the proportion is normal

hence the margin of error for a 95% confidence interval is se*z_alpha/2

where z_alpha/2 is the critical value that is the upper alpha/2 point of a N(0,1) distribution

for 95% confidence interval alpha=0.05

hence z_0.025=1.96 [using MINITAB]

hence the ragin of error is 0.00411*1.96=0.00806   [answer]

d) hence the 95% confidence interval for the population proportion is

[p-margin of error,p+margin of error]=[0.01710-0.00806,0.01710+0.00806]=[0.00904,0.02516] [answer]

e) so from the confidence interval we find that the proportion of victims lies within [0.00904,0.02516]

that is from 0.904% to 2.516% of all adults were victims which is definitely less than 10%

hence the conclusion is Yes, fewer than 10% of all adults were victims [option B] [answer]