The excel file comprises of BMI results of Women-Kg/m2 and Mean Years in School for Women aged 25 years and older. In this study I will be interested in making guesses based on separate sheets, Data 1 and Data 2. Data 1 sheet comprises of the women body mass index (BMI) measured in Kg/m 2 for last three decades. The women BMI was collected from 174 countries globally. Looking at the data, I guess that the cross-country average for women BMI is 25 Kg/m 2 . Also, the log of the women body mass index cross country average will be 1.39794. For Data 2 comprises of mean years in school for women who are aged 25 years and older. The data consists of the mean number of years women spend in school from 174 countries worldwide. Having a close look into the data I guess that the average school years is 5 years. Also, the log of the women mean school years cross countries will be 0.700465 units.
Figure 1 : Boxplot for women’s MBI (Kg/m2)
The graph above shows the boxplot for women’s BMI . It is a standardized way of displaying the distribution of women’s BMI data based on a five-number summary ; minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The boxplot shows that there are no outliers in the data, since there is no extreme value. It also shows that the data is positively skewed because the mean is less compared to the median.
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Figure 2 : Boxplot for women’s MBI (Kg/m2) log scale
The boxplot above is for the log scale of the women BMI. It indicates that there is no outlier in the data because there is no extreme value. The boxplot shows that the data is positively skewed, because the mean and the median are equal.
Figure 3 : Women’s MBI (Kg/m2)
The histogram above shows the distribution of body mass index of the women. It shows that the data is normally distributed. This is because the shape of the graph is symmetrical.
Mean School Years
Figure 4 : Boxplot for mean school years
The graph above shows the boxplot for women’s mean school years . The boxplot shows that there are no outliers in the data, since there is no extreme value. It also shows that the data is negatively skewed because the mean is lesser, when compared to the median. Further, the data for the log mean school years shows that there are outliers in the data that is -0.72204 and -0.527899. The data is ten positively skewed since the mean is greater than the median.
Figure 5 : Histogram for mean school years
The graph above shows the distribution of the mean school years. It is evident that the data is negatively skewed, because majority of the values are located on left side of the histogram. This mean implies that most of the women have few school years.
Correlation
The correlation coefficient linking the Women's BMI and mean years in school is 0.0564 units. This implies that there is a positive association linking the women's BMI and mean years in school. The relationship is very weak, because the correlation coefficient is less than 0.5 units. Th scatterplot below shows the direction of the relationship that is positive. This implies that an increase in the body mass index of the women will result to a rise in the mean years in school.
Figure 6 : Scatterplot
Based on the interpretation of the scatterplot above, the relationship is spurious. This is because the women body mass index and mean school years are associated but not causally related. It may be caused by coincidence or presence of the third factor.
Confidence Interval
The confidence interval for the population mean of women BMI is (24.1, 24.8). This implies that we are 95 % confident that the population mean of women BMI is between 24.1 and 24.8, based on 174 samples. Further, the confidence interval for the population mean of mean school years is (4.99, 6.03). This implies that we are 95 % confident that the population mean of mean school years is between 4.99 and 6.03, based on 174 samples. The interval is not valued, because we used the critical value for the t-distribution.
We use the hypothesis testing to establish if the educate guess is the true mean for the population. Here, we hypothesize the mean is same to 25 kg/m 2 . We test the following hypothesis.
H0: μ = 25
H1: μ ≠ 25
The significance level, alpha = 5 % (0.05).
The sample mean is 24.41, with an associated p-value of 0.001182 units. We compare the p-vale with the significance level, alpha = 0.05. Since the p-value is smaller compared the alpha = 0.05, we reject the null hypothesis. Hence, we deduce that the population mean is not equal to 25 kg/m 2 .
For the second data for mean school years, we hypothesize that the mean will be 5 units. We hypothesis test to establish if the mean school years is the true mean for the population. The following is the hypothesis.
H0: μ = 5
H1: μ ≠ 5
The sample mean is 5.511units, with associated p-value of 0.055448 units. We compare the p-vale with the significance level, alpha = 0.05. Since the p-value is greater compared the alpha = 0.05, we fail to reject the null hypothesis. Hence, we deduce that the population mean is not equal to 5 years.
References
Gorman, K., & Johnson, D. E. (2013). Quantitative analysis. The Oxford handbook of sociolinguistics , 214-240.
MacRae, A. W. (2019). Descriptive and inferential statistics. Companion Encyclopedia of Psychology: Volume Two , 1099.
