What is the standard error for this problem, not using the pooled values 7.24 Diamonds, Part I. Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity,color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is notsmooth. For example, the difference between the size of a 0.99 carat diamond and a 1 carat diamond isundetectable to the naked human eye, but the price of a 1 carat diamond tends to be much higher than theprice of a 0.99 diamond. In this question we use two random samples of diamonds, 0.99 carats and 1 carat,each sample of size 23, and compare the average prices of the diamonds. In order to be able to compareequivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, fora 0.99 carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100. Thedistributions and some sample statistics are shown below.2080Conduct a hypothesis test to evaluate if there is a differencebetween the average standardized prices of 0.99 and 1 caratdiamonds. Make sure to state your hypotheses clearly, checkrelevant conditions, and interpret your results in context ofthe data.60E0.99 carats 1 carat40Mean$44.51$56.81SD$13.32$16.1320n23231 caratPoint price (in dollars)0.99 carats

From the given information we find the standard error without using pooled value.

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What is the standard error for this problem, not using the pooled values

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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Question

What is the standard error for this problem, not using the pooled values

7.24 Diamonds, Part I. Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity,
color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not
smooth. For example, the difference between the size of a 0.99 carat diamond and a 1 carat diamond is
undetectable to the naked human eye, but the price of a 1 carat diamond tends to be much higher than the
price of a 0.99 diamond. In this question we use two random samples of diamonds, 0.99 carats and 1 carat,
each sample of size 23, and compare the average prices of the diamonds. In order to be able to compare
equivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, for
a 0.99 carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100. The
distributions and some sample statistics are shown below.20
80
Conduct a hypothesis test to evaluate if there is a difference
between the average standardized prices of 0.99 and 1 carat
diamonds. Make sure to state your hypotheses clearly, check
relevant conditions, and interpret your results in context of
the data.
60
E
0.99 carats 1 carat
40
Mean
$44.51
$56.81
SD
$13.32
$16.13
20
n
23
23
1 carat
Point price (in dollars)
0.99 carats

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