t Test for Dependent Means. A psychologist is trying to understand the effect of giving information about alcohol use to college students has on their alcohol consumption. To do so, the psychologist assesses freshman student’s knowledge of alcohol before an informational lecture and then assesses their knowledge again after the informational lecture. Using the information provided, conduct an appropriate t test to determine whether or not the informational lecture changes freshman student’s knowledge about alcohol. Knowledge Before Knowledge After 10 15 3 18 9 20 6 19 4 13 Step 1) Null Hypothesis (H0): Research Hypothesis (H1): Step 2) Determine the characteristics of the comparison distribution. Degrees of freedom = df = ____ Mean of the differences = M = _ Mean of the population = μ = Sum of Squared Deviations of the differences = SS = _ Population variance estimated from the differences = S2 = ___ Variance of the comparison distribution = S2M = _ Standard deviation of the comparison distribution = SM = _ Step 3) Determine the cutoff score on the t distribution (use a 0.05 p value). Cut-off = _ Step 4) Determine your sample’s t score. t = _______ Step 5) Decide whether or not to reject null hypothesis. What do you conclude?

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Description: t Test for Dependent Means. A psychologist is trying to understand the effect of giving information about alcohol use to college students has on their alcohol consumption. To do so, the psychologist assesses freshman student’s knowledge of alcohol be

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter7: Percents

Section7.1: Percents And Fractions

Problem 57E

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t Test for Dependent Means. A psychologist is trying to understand the effect of giving information about alcohol use to college students has on their alcohol consumption. To do so, the psychologist assesses freshman student’s knowledge of alcohol before an informational lecture and then assesses their knowledge again after the informational lecture. Using the information provided, conduct an appropriate t test to determine whether or not the informational lecture changes freshman student’s knowledge about alcohol.

Knowledge Before	Knowledge After
10	15
3	18
9	20
6	19
4	13

Step 1)

Null Hypothesis (H₀):
Research Hypothesis (H₁):

Step 2) Determine the characteristics of the comparison distribution.

Degrees of freedom = df = ________
Mean of the differences = M = _________
Mean of the population = μ = ________
Sum of Squared Deviations of the differences = SS = _________
Population variance estimated from the differences = S² = ___________
Variance of the comparison distribution = S²_M = _________
Standard deviation of the comparison distribution = S_M= _________

Step 3) Determine the cutoff score on the t distribution (use a 0.05 p value).

Cut-off = _________

Step 4) Determine your sample’s t score.

t = _{___________}

Step 5) Decide whether or not to reject null hypothesis. What do you conclude?

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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