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INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY26The scale of measure for all the data variables are ratio. This is because all the difference in valueis significant as well as the ratio.T-test for two comparing training resultsThe hypothesis for this test is;H0: µ1 = µ2Ha: µ1 ≠ µ2t-Test: Two-Sample Assuming Unequal VariancesGroup A Prior Training ScoresGroup B Revised Training ScoresMean69.7903225884.77419355Variance122.00449526.96456901Observations6262Hypothesized Mean Difference0Df87t Stat-9.666557191P(T<=t) one-tail9.69914E-16t Critical one-tail1.662557349P(T<=t) two-tail1.93983E-15t Critical two-tail1.987608282T-test for difference in meanThe average result for training A is 69.79, while that for B is 84.77, the critical value for two-tailed, 1.9876 is greater than the p-value for two-tailed = 1.93983E-15, this implies that there is significant difference in mean for the two samples. The p-value is also smaller than the level of significance α = 0.05, thus we reject H0 and conclude that the population mean for the training outcomes is significantly different. The revised training is superior.The two samples were drawn from normally distributed populations as indicated by the shapes of the histograms. The sample size is also large enough to be used for test since there are 62 pairs of observations. The scale of measurement for the data is ratio since they are training results. The data were drawn using random sampling technique as the run tests indicate randomness. Thus the test is valid since the assumptions are met (Xue, & Titterington, 2011).
INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY27Group A Prior Training Scores50556065707580859095Frequency4531191011351Frequency Distributions for Group A training resultsGroup B Revised 74767880828486889092949698Frequency04376911774121Frequency Distributions for Group B training results051015Group AFrequencyGroup B Revised Training ScoresFrequency051015Group BFrequencyGroup A Prior Training ScoresFrequencyHistogram representation for both variablesGroup A Prior Training Group B Revised Training Mean69.79032258Mean84.77419355Standard Error1.402788093Standard Error0.659478888Median70Median85Mode80Mode85Standard Deviation11.04556449Standard Deviation5.192741955Sample Variance122.004495Sample Variance26.96456901Kurtosis-0.77667598Kurtosis-Skewness-Skewness0.144084526
INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY28Range41Range22Minimum50Minimum75Maximum91Maximum97Sum4327Sum5256Count62Count62Confidence Level (95.0%)2.805048156Confidence Level (95.0%)1.318709538Descriptive statistics for the variables Measures of central TendencyThe mean mode and media for both variables indicate a slight variations and thus indicating that the population from which the data was draw follow a normal distribution. This can also be observed from the shapes of the histograms. The histograms are bell shaped.