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.)

Identify Given Values: Identify the given values. Confidence level (c) = 0.90 Sample mean (bar(x)) = 15.2 Population standard deviation (sigma) = 5.0 Sample size (n) = 90Find Z-Score: Find the z-score corresponding to the given confidence level. 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. E = z * (sigma / sqrt(n)) E = 1.645 * (5.0 / sqrt(90)) E = 1.645 * (5.0 / 9.4868) E = 1.645 * 0.5270 E = 0.8666Calculate Confidence Interval Bounds: Calculate the lower and upper bounds of the confidence interval. Lower bound = bar(x) - E Lower bound = 15.2 - 0.8666 Lower bound = 14.3334 Upper bound = bar(x) + E Upper bound = 15.2 + 0.8666 Upper bound = 16.0666 Round both bounds to one decimal place. Lower bound = 14.3 Upper bound = 16.1

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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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Grade 6

Calculate mean absolute deviation

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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

90 \%

confidence interval for

\mu

( \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 = $16.1$