Q. 67 Determine which of the following... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 7: Q. 67 (page 431)

Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.
a. When the sample size is large, the mean of $\overset{炉}{X}$ is approximately equal to the mean of $X$ .
b. When the sample size is large, $\overset{炉}{X}$ is approximately normally distributed.
c. When the sample size is large, the standard deviation of $\overset{炉}{X}$ is approximately the same as the standard deviation of $X$ .

Short Answer

Expert verified

All the statements are true.

The statements a,b,c of the question are true.

Step by step solution

Part (a) Step 1: Given Information

We need to find this statement is true or false. " When the sample size is large, the mean of $\overset{炉}{X}$ is approximately equal to the mean of $X$ ."

Part (a) Step 2: Explanation

When the sample size is big, the central limit theorem holds true. The sample mean is almost equal to $\overset{炉}{X}$ .

Part (b) Step 1: Given Information

We need to find this statement is true or false. " When the sample size is large, $\overset{炉}{X}$ is approximately normally distributed."

Part (b) Step 2: Explanation

When the sample size is big, the central limit theorem holds true. Then $\overset{炉}{X}$ has a roughly normal distribution.

Part (c) Step 1: Given Information

We need to find the statement is true or false. " When the sample size is large, the standard deviation of $\overset{炉}{X}$ is approximately the same as the standard deviation of $X$ ."

Part (c) Step 2: Explanation

When the sample size is big, the central limit theorem holds true. The standard deviation of $\overset{炉}{X}$ is hence roughly equal to the sample mean's standard deviation.

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Red	Orange	Yellow	Brown	Blue	Green
$0.751$	$0.735$	$0.883$	$0.696$	$0.881$	$0.925$
$0.841$	$0.895$	$0.769$	$0.876$	$0.863$	$0.914$
$0.856$	$0.865$	$0.859$	$0.855$	$0.775$	$0.881$
$0.799$	$0.864$	$0.784$	$0.806$	$0.854$	$0.865$
$0.966$	$0.852$	$0.824$	$0.840$	$0.810$	$0.865$
$0.859$	$0.866$	$0.858$	$0.868$	$0.858$	$1.015$
$0.857$	$0.859$	$0.848$	$0.859$	$0.818$	$0.876$
$0.942$	$0.838$	$0.851$	$0.982$	$0.868$	$0.809$
$0.873$	$0.863$			$0.803$	$0.865$
$0.809$	$0.888$			$0.932$	$0.848$
$0.890$	$0.925$			$0.842$	$0.940$
$0.878$	$0.793$			$0.832$	$0.833$
$0.905$	$0.977$			$0.807$	$0.845$
	$0.850$			$0.841$	$0.852$
	$0.830$			$0.932$	$0.778$
	$0.856$			$0.833$	$0.814$
	$0.842$			$0.881$	$0.791$
	$0.778$			$0.818$	$0.810$
	$0.786$			$0.864$	$0.881$
	$0.853$			$0.825$
	$0.864$			$0.855$
	$0.873$			$0.942$
	$0.880$			$0.825$
	$0.882$			$0.869$
	$0.931$			$0.912$
				$0.887$

91影视

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Explanation

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