efer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterval (13.046,22.15) x=17.598 Sx=16.01712719 n=50 a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly. Mbps<μ<Mbps (Round to two decimal places as needed.) b. Identify the best point estimate of μ and the margin of error. The point estimate of μ is Mbps. (Round to two decimal places as needed.) The margin of error is E=Mbps. (Round to two decimal places as needed.) c. In constructing the confidence interval estimate of μ, why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution? A. Because the sample size of 50 is greater than 30, the distribution of sample means can be treated as a normal distribution. B. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval. C. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution. D. Because the population standard deviation is known, the normal distribution can be used to construct the confidence interval.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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efer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below.	TInterval
(13.046,22.15) x=17.598 Sx=16.01712719 n=50

a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.

__Mbps<μ<__Mbps

(Round to two decimal places as needed.)

b. Identify the best point estimate of μ and the margin of error.

The point estimate of μ is

__Mbps.

(Round to two decimal places as needed.)

The margin of error is

E=__Mbps.

(Round to two decimal places as needed.)

c. In constructing the confidence interval estimate of μ,
why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution?

Because the sample size of 50 is greater than 30, the distribution of sample means can be treated as a normal distribution.

Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval.

Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.

Because the population standard deviation is known, the normal distribution can be used to construct the confidence interval.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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$\mathbf{Solution}$

$\mathrm{given:}$

$\mathrm{\mathrm{Confidence\;intreval:}\;(13.046,22.15)\Rightarrow Lower\;limit=13.046,\;Upper\;limit=22.15}$

$\mathrm{Sample\;mean\;(\bar x)=17.598}$

$\mathrm{Sample\;standard\;deviation\;\left (S_{x} \right )=16.01712719}$

$\mathrm{Sample\;size\;\left (n \right )=50}$

$\mathbf{{\color{Blue} a}})\;\;\mathbf{{\color{Red} 13.046}\;Mbps<\mu<{\color{Red} 22.15}\;Mbps}$

$\mathrm{Since,\;Confidence\;interval\;for\;population\;mean,\mu=Lower\;limit<\mu<Upper\;limit}$

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