# Data Analysis Assignment – Math Problem Example

Question 1:a. Mean and standard deviation: Given that the sample was randomly selected then the sample means is expected to be unbiased and therefore depict the population means, this means that the sample mean of the random sample will be an unbiased estimator of the population mean, in this case therefore we determine the sample mean, the results below shows the SPSS output where n =258:TotalMeanStd. Deviation57.178317.97748Sum14752.00In the above case n = 258, the population means is mean is 57.1783 and standard deviation is 17.97748B. confidence interval: The confidence interval is calculated as follows according to Stuart (1998): P{ [ X – ST] ≤ X≤ [ X+ ST]} = 90%Where X is the mean, S is the standard deviation and T is the T statistic at 90% level, we substitute our formula as follows: P{ [57.1783 – (17.97748)( 2.32635)] ≤ 57.1783≤ [57.1783 + (17.97748)( 2.32635)]} = 90%P{15.35639 ≤ 57.1783≤ 99.00021} = 90%This means that we are 90% confident that the populations mean of exam results lies between 15.35639 and 99.00021.C.

justification of the formula: The above formula is used in the determination of a confidence interval, the formula uses the mean, standard deviation and T statistic value, the standard deviation is a measure of dispersion of the mean, by constructing a confidence interval we determine the deviation of the mean given a level of confidence, therefore the confidence interval above states that there is a 90% probability that the mean lies between 15.35639 and 99.00021.D.

sample means for Australian and non Australian residentsThe following is the SPSS output for the sample means of the different countries: ReportExamCountryMeanNStd. Deviation160.025411815.80461656.21749219.80167752.45244219.18231849.0000611.71324Total57.178325817.97748Means: CountryMean160.0254656.2174752.4524849.0000Total57.1783From the above output it is evident that country 1 mean is higher than in any other country. E.

standard deviation: CountryStd. Deviation115.80461619.80167719.18231811.71324Total17.97748The standard deviations are also summarized in the above table. F. difference in means: In this case we test whether exam mean results in Australia are higher than in non Australian residents, we assume that country 1 represents Australia, Null hypothesis: H0: a = bAlternative hypothesis: Ha: a > bWhere a is the mean for Australia exam results, and b is mean result for the other country. The following is the SPSS output: Country 1 and 6:Group StatisticsCountryNMeanStd. DeviationStd. Error MeanExam111860.025415.804611.4549369256.217419.801672.06447Independent Samples TestLevene's Test for Equality of Variancest-test for Equality of MeansFSig. tdfSig.

(2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerUpperExamEqual variances assumed4.642.0332.517158.0137.573043.009011.6299813.51611Equal variances not assumed2.29661.939.0257.573043.29815.9800014.16608Country 1 and 7Group StatisticsCountryNMeanStd. DeviationStd. Error MeanExam111860.025415.804611.4549374252.452419.182312.95989Independent Samples TestLevene's Test for Equality of Variancest-test for Equality of MeansFSig. tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerUpperExamEqual variances assumed4.642.0332.517158.0137.573043.009011.6299813.51611Equal variances not assumed2.29661.939.0257.573043.29815.9800014.16608Country 1 and 8:Group StatisticsCountryNMeanStd. DeviationStd. Error MeanExam111860.025415.804611.454938649.000011.713244.78191Independent Samples TestLevene's Test for Equality of Variancest-test for Equality of MeansFSig. tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerUpperExamEqual variances assumed. 765.3831.683122.09511.025426.55283-1.9465723.99741Equal variances not assumed2.2065.966.07011.025424.99835-1.2218223.27266We reject the null hypothesis H0: a = b and accept the alternative hypothesis that Ha: a > b in all the cases and therefore conclude that the performance of Australian residents is higher than in the other countries. Question 2:A.

male broken down into faculty and country: Faculty1CountCountry167284041208198138011B. female broken down into faculty and country: Faculty1CountCountry16729446260114008400C. proportion: 1 =Business, 2=Sciences, 3=Engineering and SurveyingMale students in group: Total in group = 258Total male =134Proportion of male = 134/258 = 51.938%Male students from Australia enrolled in the business faculty: Male from Australia = 59Male enrolled in business = 28Proportion = 28/59 = 47.4576%Female in science facultyFemale = 124Science faculty females= 37Proportion = 37/124 = 29.84%D.

confidence interval: We assume that the sample considered in this study was randomly selected and therefore represents the entire population, in this case therefore we consider the sample for overseas students in analyzing this relationship, the following is a summary of the