The Practice of Statistics for AP - 4th Edition

4th Edition

ISBN: 9781429245593

Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.

Publisher: Macmillan Higher Education

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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 + ...

Chapter 10.2, Problem 44E

(a)

To determine

To Explain: That the centres are similar or different from the two groups and the spreads are identical or distinct from the two groups.

(a)

Expert Solution

Answer to Problem 44E

Centers: different

Spread: different

Explanation of Solution

Given:

The Practice of Statistics for AP - 4th Edition, Chapter 10.2, Problem 44E , additional homework tip 1

The centre lies between the dot most to the left and the dot most to the right, approximately in the centre. Then it is noticed that the centre is more to the right than to the left of the upper dot plot, so the centres seem to be different. The spread is the difference between the leftmost dot and the rightmost dot. Then it is noticed that the spread tends to be more than the spread for the bottom dot plot for the top dot plot, and therefore the spread tends to be different.

(b)

To determine

To construct: and explain a 95 percent confidence interval for the difference in the mean length of these two types flowers.

(b)

Expert Solution

Answer to Problem 44E

(2.5538, 4.4828)

Explanation of Solution

Given:

The Practice of Statistics for AP - 4th Edition, Chapter 10.2, Problem 44E , additional homework tip 2

Formula used:

For the confidence interval

$(x¯1−x¯2)±tα/2×s12n1+s22n2$

Calculation:

The computed mean is

$x¯1=39.6983x¯2=36.18$

The computed variance is

$s1=1.7865s2=0.9753$

Finding the degrees of freedom is

$df=min(n1−1,n2−1)=min(23−1,15−1)=14$

Determine $t∗$ with $df=14$ and $c=95%$

$t∗=2.145$

Confidence interval for $μ1−μ2$ are:

$(x¯1−x¯2)−tα/2×s12n1+s22n2=(39.6983−36.18)−2.145×1.7865223+0.9753215=2.5538$

$(x¯1−x¯2)+tα/2×s12n1+s22n2=(39.6983−36.18)+2.145×1.7865223+0.9753215=4.4828$

There is 95% trust that there is a significant difference between 2.5538 and 4.4828.

(c)

To determine

To Explain: The interval confirms the researcher's assumption that the average length of the two flower varieties is different.

(c)

Expert Solution

Explanation of Solution

From the part (b):

(2.5538. 4.4828)

The confidence interval does not include 0, which means that the mean difference is more likely to be non-zero and that the interval also supports the assumption that the two varieties have different lengths.

Chapter 10.2, Problem 43E

Chapter 10.2, Problem 45E

Chapter 10 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 10.1 - Prob. 1.1CYU Ch. 10.1 - Prob. 1.2CYU Ch. 10.1 - Prob. 1.3CYU Ch. 10.1 - Prob. 1.4CYU Ch. 10.1 - Prob. 2.1CYU Ch. 10.1 - Prob. 3.1CYU Ch. 10.1 - Prob. 3.2CYU Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E

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