Statistical analysis is plays an important role in the process of decision making. For any type of data set, we use the statistical analysis for the different variables for finding the facts regarding data. Here, we have to analyze the data regarding the two variables sunshine and sunlight for the Liverpool city in United Kingdom. We have to use the descriptive statistics for these variables for the data for the sunshine and sunlight from the year 1981. The descriptive statistics gives us general idea about the nature of data. Also, we have to use the scatter diagrams for finding the relationship between the two variables. Also we have to use testing of hypothesis for checking the different claims regarding the variables included in the data set. We have to use the Mann-Whitney test for median, two sample t test for the population means for checking the significant difference between the two medians and means. Let us see this statistical analysis in detail given as below:
An objective for this study is to use of descriptive statistics and testing of hypothesis for making decisions about the variables included in the study. Also, by using the different techniques of testing of hypothesis we have to check the different claims given as below:
Is there any significant difference between the two medians?
Is there any significant difference between the two means?
From the scatter diagram, it is observed that there is a positive relationship exists between the average monthly sunshine hours and average monthly sunlight hours. The average sunshine hours for the February month is given as 65.15 with the standard deviation of 3.54 while the average sunlight hours for the February month is given as 73.85 with the standard deviation of 4.84.
From the comparison of the above two seven year moving average plots, it is observed that there is a larger variation for the sunshine data than the sunlight data. Also, the prediction line shows that there is more variation in the sunshine data than the sunlight data. The overall pattern for the sunshine and sunlight data has the same pattern of variation and this facts show that there is a relationship between the sunshine data and sunlight data.
The Mann-Whitney test is used for checking the significant difference between the medians. The test is significant at 5% level of significance. This means we conclude that there is a significant difference between the medians of the hours of sunshine. Two sample t test for population means is used for checking the significant difference between the population means. For this test we get the p-value as 0.00, so the test is significant at 5% level of significance. So, we conclude that there is a significant difference between the means of the hours of sunshine.
Results are always sensitive for the observations included in the data set and if any artificial errors occur in the data then this may impact on the results of the hypothesis tests used for checking the claims. Due to these observations the values for the mean, standard deviations would be change and this will results into increasing or decreasing the value of test statistics and P-value. We take the decision based on the P-value and this fact bias out results regarding the null hypothesis. So, it is important to avoid these types of errors in the data set for research studies.
The chi square test for independence is used for investigating the preferences on the alternative uses of farmland for the Biofuels for transport, Photovoltaic arrays and Wind turbines. For this test we get the p-value = 0.00 approximately which is less than alpha value or level of significance 0.05, so we reject the null hypothesis that two categorical variables are independent. This means we conclude that two categorical variables are not independent.
The average sunshine hours for the February month is given as 65.15 with the standard deviation of 3.54 while the average sunlight hours for the February month is given as 73.85 with the standard deviation of 4.84.
We conclude that there is a significant difference between the medians of the hours of sunshine.
We conclude that there is a significant difference between the means of the hours of sunshine.
The chi square test for independence for investigating the preferences on the alternative uses of farmland for the Biofuels for transport, Photovoltaic arrays and Wind turbines shows that two categorical variables are not independent.
Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.
Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd.
Degroot, M. and Schervish, M. (2002). Probability and Statistics. Addison - Wesley.
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