Statistics Essay - Calories

Calorie is a measure of the energy contained in food consumed. Contrary to beliefs held, a calorie from fat or carbohydrate is the same. As a result, some fat-free foods contain almost the same quantity of calories as everyday foods. Thus, reduction of fat-rich foods in a diet does not always reduce the number of calories taken. Fat, however, has almost double the amount of calories contained in protein and carbohydrate. It is, therefore, imperative that reduction of fat in food is crucial in energy balance. The objective of the analysis is to compare the quantities of energy contained in regular foods in comparison to their healthy alternatives. The variables of interest are calories, saturated fat, cholesterol and sodium. These variables present the platform for our comparison (National Institute of Health)..
We are interested in establishing if the energy quantity of regular foods are significantly similar to the recommended energy quantities of healthy foods. The null hypothesis is usually neutral and as expected the null hypothesis will be “The energy quantities of regular foods is not significantly different from the energy quantities of healthy foods”. The alternative hypothesis will be “There is a significant difference between the energy quantities of regular foods and healthy foods”.
The mean quantity of calories contained in regular foods is 368 as opposed to the mean quantity of calories contained in healthy foods is given by 258.6. This is a very big difference, and it is expected that even with 95% confidence interval the confidence intervals of the mean calorie values for regular and healthy food do not coincide. Therefore, there is a significant difference between the mean calorie values for regular and healthy foods (Lehmann, & Romano, 2005).
The mean saturated fat value for regular food is almost twice the value for healthy food. It is expected that the null hypothesis is rejected in favor of the alternative hypothesis and it is concluded that there is a significant difference between the mean saturated fat value for regular food and the mean saturated value for healthy food.
The mean cholesterol value for regular food is 40 and the standard error of the mean is obtained by dividing the standard deviation by the sample size thus it can be approximated to be 0.5 for the healthy food and 1 for regular food. When these values are added to the mean, the confidence intervals do not coincide and as such it can be concluded that the mean cholesterol values for regular food is significantly different from the mean cholesterol value for healthy food (Lehmann, & Romano, 2005).
The mean sodium value for healthy food is 590, compared to the mean sodium value for healthy food that is 850. Incorporating the standard errors of the mean, the possible limits within which the mean lies do not coincide. As such there is no possibility that the means of the sodium levels are the same for healthy and regular foods. Thus, the null hypothesis is rejected.

References

Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses. New York: Springer.
National Institutes of Health. Limit Fat and Sugar. U.S Department of Health & Human Services. Retrieved from: http://www.nhlbi.nih.gov/health/educational/wecan/eat-right/limit-fat-sugar.htm