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Name: The average GPA of a random sample of 40 college students who take eve
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Description: The average GPA of a random sample of 40 college students who take evening classes was calculated to be 3.38 with a standard deviation of 0.04. The average GPA of a random sample of 23 college students who take daytime classes was calculated to be 3.

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 average GPA of a random sample of 40 college students who take evening classes was calculated to be 3.38 with a standard deviation of 0.04. The average GPA of a random sample of 23 college students who take daytime classes was calculated to be 3.35 with a standard deviation of 0.02. Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the .01 significance level.

Claim: Select an answer u 1 u 2 p 1≠p 2 u 1 = u 2 p 1 ≤ p 2 p 1 p 2 p 1 = p 2 which corresponds to Select an answer H0: u 1 = u 2 H0: u 1 ≤ u 2 H1: u 1 p 2 H1: p 1 u 2 H1: u 1≠u 2 H0: u 1≠u 2

Opposite: Select an answer u 1≠u 2 p 1≠p 2 p 1 > p 2 p 1 ≤ p 2 p 1 ≥ p 2 u 1 u 2 u 1 ≥ u 2 which corresponds to Select an answer H1: u 1≠u 2 H1: u 1 > u 2 H0: u 1 ≤ u 2 H0: u 1 = u 2 H1: p 1 = p 2 H1: p 1 ≥ p 2 H0: p 1 > p 2 H1: u 1 < u 2 H0: p 1≠p 2 H1: p 1 <= p 2 H0: u 1≠u 2

The test is: Select an answer left-tailed right-tailed two-tailed

The test statistic is: tt = (to 2 decimals)

The P-value is: Select an answer P-value < 0.005 0.005 < P-value < 0.01 0.01 < P-value < 0.025 0.025 < P-value < 0.05 0.05 < P-value < 0.1 0.1 < P-value

Based on this we: Select an answer Fail to reject the null hypothesis Accept the null hypothesis Cannot determine anything Reject the null hypothesis

Conclusion There Select an answer does does not appear to be enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students.

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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