A random sample of 225 items from a population results in 60% possessing a given characteristic.Using this information, the researcher constructs a 90% confidence interval to estimate the population proportion.The resulting confidence interval is _______.
A)0.546 to 0.654
B)0.536 to 0.664
C)0.596 to 0.604
D)0.571 to 0.629
E)0.629 to 0.687

Question

Quizplus · Accepted Answer

The sample proportion is 60% or 0.6. For a 90% confidence interval, the Z-score is approximately 1.645. The standard error (SE) is calculated using the formula SE = sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size. Plugging in the values, SE = sqrt[(0.6*0.4)/225] = 0.032. The margin of error (ME) is Z*SE = 1.645*0.032 = 0.05262. Therefore, the confidence interval is 0.6 ± 0.05262, which is approximately 0.547 to 0.653, closest to option A) 0.546 to 0.654.

A Random Sample of 225 Items from a Population Results