A two-sample t-test for a difference in means was conducted to investigate whether there is a statistically significant difference in the average amount of fat found in low-fat yogurt and the average amount of fat found in nonfat yogurt. With all conditions for inference met, the test produced a test statistic of t=2.201 and a p-value of 0.027. Based on the p-value and a significance level of α=0.05, which of the following is the correct conclusion? Reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant. A Reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant. B Fail to reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant. C Fail to reject the null hypothesis because p>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant. D Fail to reject the null hypothesis because p>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant.

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Description: A two-sample t-test for a difference in means was conducted to investigate whether there is a statistically significant difference in the average amount of fat found in low-fat yogurt and the average amount of fat found in nonfat yogurt. With all con

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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A two-sample t-test for a difference in means was conducted to investigate whether there is a statistically significant difference in the average amount of fat found in low-fat yogurt and the average amount of fat found in nonfat yogurt. With all conditions for inference met, the test produced a test statistic of t=2.201 and a p-value of 0.027.

Based on the p-value and a significance level of α=0.05, which of the following is the correct conclusion?

Reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant.

A
Reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant.

B
Fail to reject the null hypothesis because p<α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant.

C
Fail to reject the null hypothesis because p>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is statistically significant.

D
Fail to reject the null hypothesis because p>α. The difference in the average amount of fat found in low-fat and nonfat yogurt is not statistically significant.

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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