The mean math achievement for the older students is 50.95. The mean math achievment for the younger students is 50.72. What might you conclude about the means?1. Mean math achievement for younger students is higher than that of older students2. Mean math achievement for older students is higher than that of younger students3. The numbers are not different, statistically speaking From these results, what might you conclude? 1. Younger students are better at math than older students2. Older students are better at math than younger students3. Younger and older students do not differ in their math achievement Group StatisticsStd. ErrorAge in YearsNMeanStd. DeviationMeanMath AchievementLower than 1355650.721612.10574.51340Higher than 1412.51362.5945444350.9457Independent Samples TestLevene's Test for Equality ofVariancest-test for Equality of Means95% Confidence Interval of theDifferenceSignificanceMeanStd. ErrorSig.tdfOne-Sided pTwo-Sided pDifferenceDifferenceLowerUpperMath AchievementEqual variances.671.413-.286997.387.775-.22410.78259-1.759811.31160assumedEqual variances notassumed-.285933.546.388.775-.22410.78553-1.765711.31750Independent Samples Effect Sizes95% Confidence IntervalPointEstimateStandardizerLowerUpperMath AchievementCohen's d12.28823-.018-.143.107Hedges' correction12.29749-.018-.143.107Glass's delta12.51362-.018-143.107a. The denominator used in estimating the effect sizes.Cohen's d uses the pooled standard deviation.Hedges' correction uses the pooled standard deviation, plus a correction factor.Glass's delta uses the sample standard deviation of the control group.

Introduction - Means - Means (average ) are used to measure across a diverse group of samples ,…

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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 mean math achievement for the older students is 50.95. The mean math achievment for the younger students is 50.72. What might you conclude about the means?

1. Mean math achievement for younger students is higher than that of older students

2. Mean math achievement for older students is higher than that of younger students

3. The numbers are not different, statistically speaking

From these results, what might you conclude?

1. Younger students are better at math than older students

2. Older students are better at math than younger students

3. Younger and older students do not differ in their math achievement

Group Statistics
Std. Error
Age in Years
N
Mean
Std. Deviation
Mean
Math Achievement
Lower than 13
556
50.7216
12.10574
.51340
Higher than 14
12.51362
.59454
443
50.9457
Independent Samples Test
Levene's Test for Equality of
Variances
t-test for Equality of Means
95% Confidence Interval of the
Difference
Significance
Mean
Std. Error
Sig.
t
df
One-Sided p
Two-Sided p
Difference
Difference
Lower
Upper
Math Achievement
Equal variances
.671
.413
-.286
997
.387
.775
-.22410
.78259
-1.75981
1.31160
assumed
Equal variances not
assumed
-.285
933.546
.388
.775
-.22410
.78553
-1.76571
1.31750
Independent Samples Effect Sizes
95% Confidence Interval
Point
Estimate
Standardizer
Lower
Upper
Math Achievement
Cohen's d
12.28823
-.018
-.143
.107
Hedges' correction
12.29749
-.018
-.143
.107
Glass's delta
12.51362
-.018
-143
.107
a. The denominator used in estimating the effect sizes.
Cohen's d uses the pooled standard deviation.
Hedges' correction uses the pooled standard deviation, plus a correction factor.
Glass's delta uses the sample standard deviation of the control group.

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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