Introduction to statistics - Essay Example

INTRODUCTION TO STATISTICS By of the of the School Q1: It has been suggested that the use of Railways and Waterways for the internal transportation of goods in Europe is in decline. The data below shows the percentage of goods moved by Railways and Waterways within a country for the years 2000 and 2009.Table 1: DataCountryRail and Waterways20002009Belgium 22.627.1Denmark 7.99.2Germany 34.733.0Ireland 3.80.6Spain 7.23.4France 24.019.0Italy 11.09.0Netherlands36.636.6Portugal 7.55.7United Kingdom1013.3(a) Do the data support the suggestion?

SOLUTIONNo; the data does not provide any evidence of decline in the use of Railways and Waterways for the internal transportation of goods in Europe. The above results can be confirmed from the linear graph shown below. We used a line graph because they are used to display data or information that changes continuously over time. Line graphs also allow us to see overall trends such as an increase or decrease in data over time. Clearly, looking at the graph we don’t observe any disparity in the data givenThe intuition can further be confirmed from the t-test significance analysis conducted.

From the table below, the percent of goods moved in the year 2000 was 16.53 while that moved in the year 2009 was 15.69, this shows no significant difference. Also from the same table (table 2), we observe that the p-value=0.206>0.05 (significance level), we thus fail to reject the null hypothesis and conclude that indeed there is no significant difference in the goods moved in the year 2000 and those moved in the year 2009.Table 2: T-Test Analysist-Test: Paired Two Sample for Meansa0.05 Year-2000Year-2009Mean16.5315.69Variance144.8823161.0166Observations1010Pearson Correlation0.

970264Hypothesized Mean Difference0df9t Stat0.861P(T 0.05 (Means are the same)T Critical one-tail1.833P(T 0.05 (Means are the same)T Critical Two-tail2.262 (b) If the data DOES support the suggestion find the mean difference and its 95% confidence limits.SOLUTION N/A (c) If the data DOES NOT support the suggestion produce a model to show the relationship between the data for 2009 and 2000 with 95% confidence limits and explain BRIEFLY what the model shows.SOLUTION In this part we regressed the 2009 data on the 2000 data since the data was found to follow a normal distribution we opted to use a parametric test (Bivariate regression analysis), we used bivariate because we only had two variables to test (simple linear regression) and the model produced is;Where represents the year 2000From table 3 below, we observe that the R-Squared (R2) is 0.

941 which implies that 94.1% of the variation in 2009 data is affected (or explained) by the 2000 data (explanatory variable)Table 3:Regression StatisticsMultiple R0.970R Square0.941Goodness of Fit >= 0.80Adjusted R Square0.934Standard Error3.258Observations10From table 4 below, we observe that the coefficient for the 2000 data is 1.023 which implies that for a unit change in 2000 data, the 2009 data changes by a factor of 1.023Table 4: ANOVA dfSSMSFP-valueRegression11364.21364.25128.550.000Residual884.90210.6128Total91449.

1  95%  Confidence Level CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept-1.221.8125-0.6720.521-5.39762.9617Year-20001.020.090211.33790.0000.81481.2309(d) Using the model, find the 95% confidence limits for the proportion expected to be moved in 2009 for a country where 20% of goods were moved in this way in 2000.SOLUTIONIf 20% of goods were moved in 2000, using our model we can compute the proportion goods moved in 2009. The model is;Thus in 2009, the proportion of goods moved was 19.242.We now find the 95% confidence limits as follows;However, for our case we use excel to compute this;The confidence as obtained from the excel is 7.460292. hence the corresponding 95% confidence limits are;i.e. the upper limit is while the lower limit is