Question

In a recent poll of 210 south Jersey households, it was found that 152 households had at least one computer. Construct a 95% confidence interval to estimate the population proportion of south Jersey. A separate survey in Philadelphia found the sample proportion of households with more than one computer to be 0.66, what kind conclusion you can made in terms of the difference in proportion between South Jersey and Philadelphia? (Your conclusion must be based on the confidence interval you obtained.

Answer 1

Sample proportion,   = 152/210 =  0.7238

Standard error of sample proportion, SE = = 0.030854

z score for 95% confidence interval is 1.96

95% confidence interval for population proportion of south Jersey households with at least one computer is,

0.7238 - 1.96 * 0.030854 to 0.7238 + 1.96 * 0.030854

0.6633 to  0.7843

Since the 95% confidence interval for population proportion of south Jersey households with at least one computer does not contain the value 0.66, we conclude that there is significant difference in proportion of households with at least one computer between South Jersey and Philadelphia.