A random sample of 130 observations produced a mean of I = 23.5 and a standard deviation s = 2.16.(a) Find a 90% confidence interval for u(b) Find a 95% confidence interval for u(c) Find a 99% confidence interval for u

Given: Sample size n = 130 mean x¯ = 23.5 Standard deviation s =…

Answered: A random sample of 130 observations…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A random sample of 130 observations produced a mean of I = 23.5 and a standard deviation s = 2.16.
(a) Find a 90% confidence interval for u
(b) Find a 95% confidence interval for u
(c) Find a 99% confidence interval for u

Expert Solution

Step 1

Given:

Sample size n = 130

mean $\bar{x}$ = 23.5

Standard deviation s = 2.16

1. 90% confidence interval for $μ$ is,

$\bar{x}$ $-$ $z \times \frac{s}{\sqrt{n}}$ $\leq μ \leq$ $\bar{x}$ $+$ $z \times \frac{s}{\sqrt{n}}$

where z value for 90% confidence interval is 1.645

$∴ 23.5 - 1.645 \times \frac{2.16}{\sqrt{130}} \leq μ \leq 23.5 + 1.645 \times \frac{2.16}{\sqrt{130}}$

$∴$ 23.1883 $\leq μ \leq$ 23.8116

Answer: 90% confidence interval for $μ$ is 23.1883 $\leq μ \leq$ 23.8116.

Step 2

2. 95% confidence interval for $μ$ is,

$\bar{x}$ $-$ $z \times \frac{s}{\sqrt{n}}$ $\leq μ \leq$ $\bar{x}$ $+$ $z \times \frac{s}{\sqrt{n}}$

where z value for 95% confidence interval is 1.960

$∴ 23.5 - 1.960 \times \frac{2.16}{\sqrt{130}} \leq μ \leq 23.5 + 1.960 \times \frac{2.16}{\sqrt{130}}$

$∴$ 23.1288 $\leq μ \leq$ 23.8712

Answer: 95% confidence interval for $μ$ is 23.1288 $\leq μ \leq$ 23.8712.

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A random sample of 130 observations produced a mean of T = 23.5 and a standard deviations = 2.16. la) Find a 90% confidence interval for u (b) Find a 95% confidence interval for (c) Find a 99% confidence interval for