Can you explain question C A random sample is drawn from a population with mean μ = 56 and standard deviation σ = 4.7. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 14 and n = 34 normally distributed? (Round the standard error to 3 decimal places.) b. Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes?multiple choice 1Yes, both the sample means will have a normal distribution.No, both the sample means will not have a normal distribution.No, only the sample mean with n = 14 will have a normal distribution.No, only the sample mean with n = 34 will have a normal distribution. c. If the sampling distribution of the sample mean is normally distributed with n = 14, then calculate the probability that the sample mean falls between 56 and 58. (If appropriate, round final answer to 4 decimal places.) ProbabilityWe cannot assume that the sampling distribution of the sample mean is normally distributed.We can assume that the sampling distribution of the sample mean is normally distributed and the probability that the sample mean falls between 56 and 58 is **Example Problem Analysis: Sampling Distribution of the Sample Mean****Problem Statement:**A random sample is drawn from a population with a mean (\( \mu \)) of 56 and a standard deviation (\( \sigma \)) of 4.7. **Question A:**Is the sampling distribution of the sample mean with \( n = 14 \) and \( n = 34 \) normally distributed? (Round the standard error to 3 decimal places.)**Solution:** | \( n \) | Expected Value | Standard Error ||--------|----------------|----------------|| 14 | 56 ✔️ | 1.256 ✔️ || 34 | 56 ✔️ | 0.806 ✔️ |The table confirms that the expected values are 56 for both sample sizes, and the standard errors are calculated as 1.256 for \( n = 14 \) and 0.806 for \( n = 34 \).**Question B:**Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes?-

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Answered: A random sample is drawn from a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Can you explain question C

A random sample is drawn from a population with mean μ = 56 and standard deviation σ = 4.7. [You may find it useful to reference the z table.]

a. Is the sampling distribution of the sample mean with n = 14 and n = 34 normally distributed? (Round the standard error to 3 decimal places.)

b. Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes?

multiple choice 1

Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal distribution.
No, only the sample mean with n = 14 will have a normal distribution.
No, only the sample mean with n = 34 will have a normal distribution.

c. If the sampling distribution of the sample mean is normally distributed with n = 14, then calculate the probability that the sample mean falls between 56 and 58. (If appropriate, round final answer to 4 decimal places.)

Probability

We cannot assume that the sampling distribution of the sample mean is normally distributed.
We can assume that the sampling distribution of the sample mean is normally distributed and the probability that the sample mean falls between 56 and 58 is

**Example Problem Analysis: Sampling Distribution of the Sample Mean**

**Problem Statement:**
A random sample is drawn from a population with a mean (\( \mu \)) of 56 and a standard deviation (\( \sigma \)) of 4.7.

**Question A:**
Is the sampling distribution of the sample mean with \( n = 14 \) and \( n = 34 \) normally distributed? (Round the standard error to 3 decimal places.)

**Solution:**

| \( n \) | Expected Value | Standard Error |
|--------|----------------|----------------|
| 14 | 56 ✔️ | 1.256 ✔️ |
| 34 | 56 ✔️ | 0.806 ✔️ |

The table confirms that the expected values are 56 for both sample sizes, and the standard errors are calculated as 1.256 for \( n = 14 \) and 0.806 for \( n = 34 \).

**Question B:**
Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes?

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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