ine students took the SAT test twice without doing any sort of preparatory course between the two tests. Their scores are listed below. Use the data to test the claim that in the population of all such students, the differences between the scores have mean 0. StudentABCDEFGHIFirst score480510530540550560600620660Second score460500530520580600560640690 a. Define the parameter A.mu Subscript d Baseline equals Mean of the second score B.mu Subscript d Baseline equals Mean of (First score - Second score) C.mu Subscript d Baseline equals Mean of the first score D.mu equals Mean score b. State the null and alternative hypotheses A.Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline not equals 0 B.Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline greater than 0 C.Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline less than 0 D.Upper H 0 : mu equals 0 Upper H 1 : mu not equals 0 c. Calculate the P-value. Which of these options is closest to its value? A.0.825 B.1.017 C.0.729 D.0.714 d. State the technical conclusion A.Reject Upper H 0 B.Do not reject Upper H 0 e. State the final conclusion A.There is not sufficient evidence to warrant rejection of the claim. B.There is sufficient evidence to warrant rejection of the claim. C.There is not sufficient sample evidence to support the claim. D.The sample data support the claim. f. Does there appear to be any difference between the first and second scores? A.Yes B.No

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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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ine students took the SAT test twice without doing any sort of preparatory course between the two tests. Their scores are listed below. Use the data to test the claim that in the population of all such students, the differences between the scores have mean 0.

Student	A	B	C	D	E	F	G	H	I
First score	480	510	530	540	550	560	600	620	660
Second score	460	500	530	520	580	600

560

640

690

a. Define the parameter

mu Subscript d Baseline equals

Mean of the second score

mu Subscript d Baseline equals

Mean of (First score - Second score)

mu Subscript d Baseline equals

Mean of the first score

mu equals

Mean score

b. State the null and alternative hypotheses

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline not equals 0

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline greater than 0

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline less than 0

Upper H 0 : mu equals 0 Upper H 1 : mu not equals 0

c. Calculate the P-value. Which of these options is closest to its value?

0.825

1.017

0.729

0.714

d. State the technical conclusion

Reject Upper H 0

Do not reject Upper H 0

e. State the final conclusion

There is not sufficient evidence to warrant rejection of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

The sample data support the claim.

f. Does there appear to be any difference between the first and second scores?

Yes

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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