Question

In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2531 subjects randomly selected from an online group involved with ears. 1161 surveys were returned. Construct a 99​% confidence interval for the proportion of returned surveys. LOADING... Click the icon to view a table of z scores. ​a) Find the best point estimate of the population proportion p. nothing

Answer 1

A point estimate of apopulation parameter is a single value of a statistic. For example, the sample mean x is a point estimate of thepopulation mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.

Here P=1161/2531=0.46 is a point estimate.

Also we calculate 99% confidence interval from given data.

Since alpha=0.01then z value is

z_α/2 = 2.5758293064

Lower Bound = p̂ - z_α/2•√p̂(1 - p̂)/n = 0.46 - (2.5758293064)(0.009906716230504955) = 0.43448199

Upper Bound = p̂ + z_α/2•√p̂(1 - p̂)/n = 0.46 + (2.5758293064)(0.009906716230504955) = 0.48551801

Confidence Interval = (0.43448199, 0.48551801)