Three students want to estimate the mean pencil weight of their schoolmates.To do this, they each randomly chose 5 schoolmates and weighed their pencils.The samples are shown in the table. (a) Fill in the sample means in the table.Do not round your answers.SamplePencil weight (in grams)Sample mean19, 7, 8, 8, 67, 8, 8, 9, 737, 9, 9, 8, 8(b) Use the table to calculate the range of the sample means.Range of sample means: I(c) The students are going to use the sample means to estimate the mean pencil weight of their schoolmates.Select all the true statements below.The closer the range of the sample means is to 0, the less confident they can be in their estimate.The farther the range of the sample means is from 0, the less confident they can be in their estimate.A single sample mean will tend to be a better estimate than the mean of the sample means.O The mean of the sample means will tend to be a better estimate than a single sample mean.

Answered: (a) Fill in the sample means in the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Three students want to estimate the mean pencil weight of their schoolmates.
To do this, they each randomly chose 5 schoolmates and weighed their pencils.

The samples are shown in the table.

(a) Fill in the sample means in the table.
Do not round your answers.
Sample
Pencil weight (in grams)
Sample mean
1
9, 7, 8, 8, 6
7, 8, 8, 9, 7
3
7, 9, 9, 8, 8
(b) Use the table to calculate the range of the sample means.
Range of sample means: I
(c) The students are going to use the sample means to estimate the mean pencil weight of their schoolmates.
Select all the true statements below.
The closer the range of the sample means is to 0, the less confident they can be in their estimate.
The farther the range of the sample means is from 0, the less confident they can be in their estimate.
A single sample mean will tend to be a better estimate than the mean of the sample means.
O The mean of the sample means will tend to be a better estimate than a single sample mean.

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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