Question

in a study if cell phone use and brain hemispheric dominance, an internet survey was emailed to 2569 subjects randomly selected from an online group involved with ears. 1200 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys.

Answer 1

To construct a 90% confidence interval for the proportion of returned surveys, we use the sample proportion and the margin of error formula. The confidence interval is (0.451, 0.482).

Step-by-step explanation:

To construct a confidence interval for the proportion of returned surveys, we will use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

In this case, the sample proportion is the proportion of returned surveys, which is 1200/2569 = 0.4666 (rounded to four decimal places). The margin of error can be calculated using the formula:

Margin of Error = Z * sqrt((p*(1-p))/n)

where Z is the Z-score corresponding to the desired confidence level (from the standard normal distribution), p is the sample proportion, and n is the sample size. For a 90% confidence level, the Z-score is approximately 1.645 (rounded to three decimal places).

Substituting the values into the formula:

Margin of Error = 1.645 * sqrt((0.4666*(1-0.4666))/2569)

After calculating the margin of error, we can construct the confidence interval:

Confidence Interval = 0.4666 ± Margin of Error

Thus, the 90% confidence interval for the proportion of returned surveys is (0.451, 0.482) (rounded to three decimal places).