A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. What conclusion can you draw from the output? The data provide sufficient evidence to reject H0 and to conclude that the mean depression score for male teens is larger than that of female teens. The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score. The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that male and female teens do not differ in mean depression score. The following is the (edited) output for the test:Two-Sample T-Test and CISample1 (м)2(F)MeanStDevSE Me an0. 660. 631127.386.951017.156.31Difference = mu (1) :- mu (2)Estimate for difference:0.23000095% lower bound for difference:-1.271079T-Test of differenceT-Value= 0.25P-Value = 0. 400DF = 210

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Description: A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depress

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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

Section13.3: Special Probability Density Functions

Problem 30E

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A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis.

What conclusion can you draw from the output?

The data provide sufficient evidence to reject H₀ and to conclude that the mean depression score for male teens is larger than that of female teens.
The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score.
The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens.
The data do not provide sufficient evidence to reject H₀, so we accept it, and conclude that male and female teens do not differ in mean depression score.

The following is the (edited) output for the test:
Two-Sample T-Test and CI
Sample
1 (м)
2(F)
Mean
StDev
SE Me an
0. 66
0. 63
112
7.38
6.95
101
7.15
6.31
Difference = mu (1) :
- mu (2)
Estimate for difference:
0.230000
95% lower bound for difference:
-1.271079
T-Test of difference
T-Value
= 0.25
P-Value = 0. 400
DF = 210

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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