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Construct the confidence interval for the population mean
mu.

c=0.90, bar(x)=15.2,sigma=5.0", and "n=90
A
90% confidence interval for
mu is
◻◻. (Round to one decimal place as needed.)

Construct the confidence interval for the population mean $\mu$ . $\newline$ $\mathrm{c}=0.90, \overline{\mathrm{x}}=15.2, \sigma=5.0 \text {, and } \mathrm{n}=90$ $\newline$ A $90 \%$ confidence interval for $\mu$ is $\square \square$ . (Round to one decimal place as needed.)

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Calculate mean absolute deviation

Full solution

Q. Construct the confidence interval for the population mean

\mu

.

\newline

\mathrm{c}=0.90, \overline{\mathrm{x}}=15.2, \sigma=5.0 \text {, and } \mathrm{n}=90

\newline

A

90 \%

confidence interval for

\mu

is

\square \square

. (Round to one decimal place as needed.)

Identify Given Values: Identify the given values. $\newline$ Confidence level $c$ = $0.90$ $\newline$ Sample mean $\bar{x}$ = $15.2$ $\newline$ Population standard deviation $\sigma$ = $5.0$ $\newline$ Sample size $n$ = $90$
Find Z-Score: Find the z-score corresponding to the given confidence level. $\newline$ For a $90\%$ confidence level, the z-score that corresponds to the upper tail ( $5\%$ in each tail for a two-tailed test) is approximately $1.645$ .
Calculate Margin of Error: Calculate the margin of error (E) using the z-score. $\newline$ $E = z \times (\sigma / \sqrt{n})$ $\newline$ $E = 1.645 \times (5.0 / \sqrt{90})$ $\newline$ $E = 1.645 \times (5.0 / 9.4868)$ $\newline$ $E = 1.645 \times 0.5270$ $\newline$ $E = 0.8666$
Calculate Confidence Interval Bounds: Calculate the lower and upper bounds of the confidence interval. $\newline$ Lower bound = $\bar{x} - E$ $\newline$ Lower bound = $15.2 - 0.8666$ $\newline$ Lower bound = $14.3334$ $\newline$ Upper bound = $\bar{x} + E$ $\newline$ Upper bound = $15.2 + 0.8666$ $\newline$ Upper bound = $16.0666$ $\newline$ Round both bounds to one decimal place. $\newline$ Lower bound = $14.3$ $\newline$ Upper bound = $16.1$

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