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Use the sample data and confidence level given below to complete parts (a) through (d).
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2671 subjects randomly selected from an online group involved with ears. 1158 surveys were returned. Construct a
99% confidence interval for the proportion of returned surveys.
国 Click the icon to view a table of z scores.
a) Find the best point estimate of the population proportion
p.

◻
(Round to three decimal places as needed.)
b) Identify the value of the margin of error
E.

E=
(Round to three decimal places as needed.)
c) Construct the confidence interval.

◻
(Round to three decimal places as needed.)

Use the sample data and confidence level given below to complete parts (a) through (d). $\newline$ In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to $2671$ subjects randomly selected from an online group involved with ears. $1158$ surveys were returned. Construct a $99 \%$ confidence interval for the proportion of returned surveys. $\newline$ 国 Click the icon to view a table of z scores. $\newline$ a) Find the best point estimate of the population proportion $p$ . $\newline$ $\square$ $\newline$ (Round to three decimal places as needed.) $\newline$ b) Identify the value of the margin of error $E$ . $\newline$ $E=$ $\newline$ (Round to three decimal places as needed.) $\newline$ c) Construct the confidence interval. $\newline$ $\square$ $\newline$ (Round to three decimal places as needed.)

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Interpret confidence intervals for population means

Full solution

Q. Use the sample data and confidence level given below to complete parts (a) through (d).

\newline

In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to

2671

subjects randomly selected from an online group involved with ears.

1158

surveys were returned. Construct a

99 \%

confidence interval for the proportion of returned surveys.

\newline

国 Click the icon to view a table of z scores.

\newline

a) Find the best point estimate of the population proportion

p

.

\newline

\square

\newline

(Round to three decimal places as needed.)

\newline

b) Identify the value of the margin of error

E

.

\newline

E=

\newline

(Round to three decimal places as needed.)

\newline

c) Construct the confidence interval.

\newline

\square

\newline

(Round to three decimal places as needed.)

Calculate Point Estimate: a) Calculate the best point estimate of the population proportion $p$ . $\newline$ Best point estimate of $p$ = number of returned surveys / total surveys sent $\newline$ $= \frac{1158}{2671}$ $\newline$ $= 0.433$
Identify Margin of Error: b) Identify the value of the margin of error $E$ using the z-score for $99$ % confidence. $Z$ -score for $99$ % confidence $\approx 2.576$ (from z-table) Standard error (SE) = $\sqrt{p(1-p)/n}$ = $\sqrt{0.433(1-0.433)/2671}$ = $0.0096$ Margin of error $E = Z \times SE$ = $2.576 \times 0.0096$ = $0.025$
Construct Confidence Interval: c) Construct the confidence interval. $\newline$ Lower bound = $p - E$ $\newline$ = $0.433 - 0.025$ $\newline$ = $0.408$ $\newline$ Upper bound = $p + E$ $\newline$ = $0.433 + 0.025$ $\newline$ = $0.458$ $\newline$ Confidence interval = $(0.408, 0.458)$

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