Question

Question 4

• A survey 550 households finds that only 18% have cable Television. (i) Find
the margin of error to construct the 95% confidence interval for the
proportion of households that have cable Television. Express your answer in
percent with two decimal places accuracy. (ii) Write the confidence interval
in the interval form as (lower limit, upper limit).

Answer 1

(i) To find the margin of error for the 95% confidence interval for the proportion of households that have cable television, we need to use the formula for the margin of error for a sample proportion. This formula is given by

ME = z * sqrt(p * (1 - p) / n)

where ME is the margin of error, z is the critical value for the desired confidence level, p is the sample proportion, and n is the sample size. In this case, p is 0.18, n is 550, and the critical value for a 95% confidence interval is 1.96. Plugging these values into the formula, we get

ME = 1.96 * sqrt(0.18 * (1 - 0.18) / 550) = 0.0215

Therefore, the margin of error for the 95% confidence interval is 2.15%.

(ii) To write the confidence interval in the interval form, we need to add and subtract the margin of error from the sample proportion. The sample proportion is 0.18, and the margin of error is 0.0215, so the confidence interval is given by

0.18 +/- 0.0215 = (0.1585, 0.2015)

Therefore, the 95% confidence interval for the proportion of households that have cable television is (0.1585, 0.2015).

Step-by-step explanation: