In: Statistics and Probability
A study of homeless men in the city revealed that out of 242 selected to be interviewed, 65 had been employed within the last year. Provide a 95% confidence interval for the proportion of all homeless men who had been employed within the past year. Interpret your result.
GIVEN:
Size of homeless men in the city selected to be interviewed
Number of homeless men who are employed within the last year
FORMULA:
The formula for 95% confidence interval for population proportion is,
where is the z critical value at 95% confidence level.
CRITICAL VALUE:
The two tailed z critical value at 95% confidence level is .
CALCULATION:
The sample proportion is given by,
The 95% confidence interval for the proportion of all homeless men who had been employed within the past year is,
The 95% confidence interval for the proportion of all homeless men who had been employed within the past year is . Thus we are 95% confident that the true proportion of all homeless men who had been employed within the past year lies between 0.2127 and 0.3245.