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Related questions with answers

Explain the difference between submergent and emergent marine plants. Describe the greatest challenge for a plant to adapt to living in the sea, and how some plant species manage that challenge.

What value is estimated with a confidence interval using the $t$ statistic?

a. The value for an unknown sample mean;

b. The value for an unknown population mean;

c. The difference between two standard deviations;

d. The difference between two sample means.

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Question

What are the mean and standard deviation of the difference Y - X between the readings? (The readings X and Y are independent.)

Solution

Verified

Step 1

1 of 2

Given:

\mu_X=2.000

\sigma_X=0.002

\mu_Y=2.001

\sigma_Y=0.001

For the linear combination $W=aX_1+bX_2$ , the mean, variance, and standard deviation are as follows:

\mu_W=a\mu_1+b\mu_2

\sigma_W^2=a^2\sigma_1^2+b^2\sigma_2^2\text{ (If $X_1$ and $X_2$ are independent)}

\sigma_W=\sqrt{a^2\sigma_1^2+b^2\sigma_2^2}\text{ (If $X_1$ and $X_2$ are independent)}

The mean and standard deviation of the difference $Y-X$ are then:

\mu_{Y-X}=\mu_Y-\mu_X=2.001-2.000=0.001

\sigma_{Y-X}=\sqrt{1^2\sigma_Y^2+(-1)^2\sigma_X^2}=\sqrt{\sigma_X^2+\sigma_Y^2}=\sqrt{0.001^2+0.002^2}=\sqrt{0.000005}\approx 0.002236

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More related questions

statistics

For the stem-and-leaf plot below, what is the maximum and what is the minimum entry?

Key: $11|2=11.2$ .

Stem	Leaf
$11$	$0$ $2$
$12$	$4$ $6$ $6$ $7$ $8$ $9$
$13$	$0$ $1$ $1$ $2$ $3$ $6$ $6$ $7$ $8$ $8$
$14$	$3$ $4$ $6$ $6$ $8$ $9$ $9$ $9$
$15$	$0$ $1$ $1$ $2$ $3$ $7$ $7$ $8$ $9$
$16$	$2$ $2$ $5$ $7$ $8$ $8$ $9$ $9$
$17$	$0$ $5$

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statistics

For the stem-and-leaf plot below, what is the maximum and what is the minimum entry?

Key: $11|2=11.2$ .

Stem	Leaf
$11$	$0$ $2$
$12$	$4$ $6$ $6$ $7$ $8$ $9$
$13$	$0$ $1$ $1$ $2$ $3$ $6$ $6$ $7$ $8$ $8$
$14$	$3$ $4$ $6$ $6$ $8$ $9$ $9$ $9$
$15$	$0$ $1$ $1$ $2$ $3$ $7$ $7$ $8$ $9$
$16$	$2$ $2$ $5$ $7$ $8$ $8$ $9$ $9$
$17$	$0$ $5$

1/7