# Перевірка статистичних гіпотез для однієї та двох вибірок, страница 4

95,0% Confidence Intervals

Standard deviation of X1: [6,95748;10,379]

Standard deviation of X2: [6,84355;9,46566]

Ratio of Variances: [0,66565;1,86687]

F-test to Compare Standard Deviations

Null hypothesis: sigma1 = sigma2

Alt. hypothesis: sigma1 NE sigma2

F = 1,09964   P-value = 0,70249

Перевіряємо статичні гіпотези за допомогою пакету Statgraphics для 1 і 3 виборки:

Summary Statistics

X1                  X3

------------------------------------------------------------

Count               50                  100

Average             10,34               12,07

Median              8,0                 12,0

Mode                3,0                 4,0

Geometric mean      7,2956              8,92676

Variance            69,3718             63,3789

Standard deviation  8,32898             7,96109

Standard error      1,1779              0,796109

Minimum             1,0                 1,0

Maximum             30,0                30,0

Range               29,0                29,0

Lower quartile      4,0                 5,0

Upper quartile      15,0                17,0

Interquartile range 11,0                12,0

Skewness            1,08537             0,547206

Stnd. skewness      3,13319             2,23396

Kurtosis            0,296347            -0,496218

Stnd. kurtosis      0,427739            -1,0129

Coeff. of variation 80,551%             65,9576%

Sum                 517,0               1207,0

------------------------------------------------------------

Comparison of Means

-------------------

95,0% confidence interval for mean of X1: 10,34 +/- 2,36707   [7,97293,12,7071]

95,0% confidence interval for mean of X3: 12,07 +/- 1,57966   [10,4903,13,6497]

95,0% confidence interval for the difference between the means

assuming equal variances: -1,73 +/- 2,76721   [-4,49721,1,03721]

t test to compare means

Null hypothesis: mean1 = mean2

Alt. hypothesis: mean1 NE mean2

assuming equal variances: t = -1,23543   P-value = 0,218627

Comparison of Standard Deviations

---------------------------------

X1                  X3

------------------------------------------------------------

Standard deviation  8,32898             7,96109

Variance            69,3718             63,3789

Df                  49                  99

Ratio of Variances = 1,09456

95,0% Confidence Intervals

Standard deviation of X1: [6,95748;10,379]

Standard deviation of X3: [6,98989;9,2482]

Ratio of Variances: [0,685218;1,82113]

F-test to Compare Standard Deviations

Null hypothesis: sigma1 = sigma2

Alt. hypothesis: sigma1 NE sigma2

F = 1,09456   P-value = 0,693477

Перевіряємо статичні гіпотези за допомогою пакету Statgraphics для 2 і 3 виборки:

Summary Statistics

X2                  X3

------------------------------------------------------------

Count               75                  100

Average             11,9067             12,07

Median              12,0                12,0

Mode                                    4,0

Geometric mean      8,61484             8,92676

Variance            63,0858             63,3789