The College Board reports that the national mean and standard deviation for high school seniors taking the SAT-V is μ =465 and σ =55. A local principal wants to know if the students in his school are performing at or above the national average on the SAT-V. He takes a random sample of 15 seniors and obtains the following scores. SAT-V 500 570 470 420 520 510 520 450 470 490 520 550 570 620 610 ∑∑ X = 7,790 Can the principal be confident that the seniors in his school performed significantly differently on the SAT-V compared to students nationally? State the correct null and research (alternative) hypotheses and conduct the appropriate statistical test to address this research question: Is there a significant difference between the national mean and sample of SAT-V? Carry out all 9 steps of hypothesis testing. Use α = .05

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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The College Board reports that the national mean and standard deviation for high school seniors taking the SAT-V is μ =465 and σ =55. A local principal wants to know if the students in his school are performing at or above the national average on the SAT-V. He takes a random sample of 15 seniors and obtains the following scores.

<SAT-V Data 2>

SAT-V
500
570
470
420
520
510
520
450
470
490
520
550
570
620
610

∑∑ X = 7,790

Can the principal be confident that the seniors in his school performed significantly differently on the SAT-V compared to students nationally?

State the correct null and research (alternative) hypotheses and conduct the appropriate statistical test to address this research question: Is there a significant difference between the national mean and sample of SAT-V? Carry out all 9 steps of hypothesis testing. Use α = .05

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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