A survey aims to compare the average reaction times (in seconds) of men (group A) and women (group B) to a certain stimulus. For this, an experiment was carried out to verify if there are differences between the sexes. Assume that the mean times follow a normal distribution and that the variance of the men's mean reaction times (σ2A) is different from the variance of women's mean reaction times (σ2B). Perform an adequate hypothesis test, considering a significance level of 5%Indivíduo12345678910Homens52667665526568 Mulheres60506050705759686165a. What range of values is the p-value in?b.There is evidence to reject H0 with the level of significance adopted?

Answered: A survey aims to compare the average…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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A survey aims to compare the average reaction times (in seconds) of men (group A) and women (group B) to a certain stimulus. For this, an experiment was carried out to verify if there are differences between the sexes. Assume that the mean times follow a normal distribution and that the variance of the men's mean reaction times (σ²A) is different from the variance of women's mean reaction times (σ²B). Perform an adequate hypothesis test, considering a significance level of 5%

Indivíduo	1	2	3	4	5	6	7	8	9	10
Homens	52	66	76	65	52	65	68
Mulheres	60	50	60	50	70	57	59	68	61	65

a. What range of values is the p-value in?

b.There is evidence to reject H0 with the level of significance adopted?

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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