Let x be a random variable representing the SAT math score of student in a state. We may assume that x has a normal distribution, and past studies have shown that the population standard deviation is 38. A large university claims the mean SAT math score for incoming freshman is 680. You suspect that this claim is too high and decide to test the claim. You select a random sample of 32 incoming freshman and find the sample mean SAT math score to be 667.4. If you assume that the population mean is 680, find the P-value corresponding to the hypothesis that the average SAT score is less than 680. A.0.03 B.0.035 C.0.042 D.0.02

It is given that Population mean = 680 Sample mean = 667.4 Population standard deviation = 38…

Answered: find the P-value corresponding to the…

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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Let x be a random variable representing the SAT math score of student in a state. We may assume that x has a normal distribution, and past studies have shown that the population standard deviation is 38. A large university claims the mean SAT math score for incoming freshman is 680. You suspect that this claim is too high and decide to test the claim. You select a random sample of 32 incoming freshman and find the sample mean SAT math score to be 667.4. If you assume that the population mean is 680, find the P-value corresponding to the hypothesis that the average SAT score is less than 680.

A.

0.03

B.

0.035

C.

0.042

D.

0.02

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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