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Use the normal distribution to find a confidence interval for a proportion
p given the relevant sample results. Give the best point estimate for
p, the margin of error, and the confidence interval. Assume the results come from a random sample.
A
99% confidence interval for the proportion of the population in Category A given that
19% of a sample of 375 are in Category A.
Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.
Point estimate
=
◻
Margin of error
=+-
◻

◻ .
The
99% confidence interval is
◻ to
◻

Use the normal distribution to find a confidence interval for a proportion $p$ given the relevant sample results. Give the best point estimate for $p$ , the margin of error, and the confidence interval. Assume the results come from a random sample. $\newline$ A $99 \%$ confidence interval for the proportion of the population in Category A given that $19 \%$ of a sample of $375$ are in Category A. $\newline$ Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places. $\newline$ Point estimate $=$ $\square$ $\newline$ Margin of error $= \pm$ $\square$ $\newline$ $\square$ . $\newline$ The $99 \%$ confidence interval is $\square$ to $\square$

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Interpret confidence intervals for population means

Full solution

Q. Use the normal distribution to find a confidence interval for a proportion

p

given the relevant sample results. Give the best point estimate for

p

, the margin of error, and the confidence interval. Assume the results come from a random sample.

\newline

A

99 \%

confidence interval for the proportion of the population in Category A given that

19 \%

of a sample of

375

are in Category A.

\newline

Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.

\newline

Point estimate

=

\square

\newline

Margin of error

= \pm

\square

\newline

\square

.

\newline

The

99 \%

confidence interval is

\square

to

\square

Calculate point estimate: Calculate the point estimate for $p$ . $\newline$ Point estimate = sample proportion = $19\%$ of $375$ . $\newline$ Point estimate = $0.19$ .
Calculate standard error: Calculate the standard error for the proportion. $\newline$ Standard error (SE) = $\sqrt{p(1-p)/n}$ . $\newline$ SE = $\sqrt{0.19 \times 0.81 / 375}$ . $\newline$ SE = $\sqrt{0.1539 / 375}$ . $\newline$ SE = $\sqrt{0.0004104}$ . $\newline$ SE = $0.02026$ .
Determine z-score: Determine the z-score for a $99\%$ confidence interval. $\newline$ Z-score for $99\%$ confidence = $2.576$ (from z-table).
Calculate margin of error: Calculate the margin of error. $\newline$ Margin of error = $Z$ -score $\times$ $SE$ . $\newline$ Margin of error = $2.576 \times 0.02026$ . $\newline$ Margin of error = $0.052189$ .
Calculate confidence interval: Calculate the confidence interval. $\newline$ Lower bound = Point estimate - Margin of error. $\newline$ Lower bound = $0.19 - 0.052189$ . $\newline$ Lower bound = $0.137811$ . $\newline$ Upper bound = Point estimate + Margin of error. $\newline$ Upper bound = $0.19 + 0.052189$ . $\newline$ Upper bound = $0.242189$ .

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