The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. The summary statistics are∑X1i=2764, ∑X21i=764410, n1=10.∑X2i=2636, ∑X22i=696144, n2=10.Assume normality and that the two samples have the same variance. Test the hypothesis that both brands of ball have equal mean overall distance. What is the degree of freedom of the T-statistic?What is the value of the pooled estimator of the standard deviation?What is the value of the T-statistic?What is the P-value?Let α=0.05, are you going to reject the null hypothesis?

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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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The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. The summary statistics are

∑X_1i=2764, ∑X²_1i=764410, n1=10.

∑X_2i=2636, ∑X²_2i=696144, n2=10.

Assume normality and that the two samples have the same variance. Test the hypothesis that both brands of ball have equal mean overall distance.

What is the degree of freedom of the T-statistic?
What is the value of the pooled estimator of the standard deviation?
What is the value of the T-statistic?
What is the P-value?
Let α=0.05, are you going to reject the null hypothesis?

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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