Summarize Results and State Conclusions

Running Head: STATISTICAL ANALYSIS AND REPORT 1

Statistical Analysis and Report

Weltee Wolo

Rasmussen College

Author Note

This paper is being submitted on February 27, 2017, for Benjamin Feinberg’s Advanced Statistics and Analytics G310/STA3140 course

Introduction

The two samples, the group of girls and that of boys are independent. Independent samples are samples which are selected randomly such that the observations of one sample do not depend on the values of the observations of the other sample. Here, the obesity prevalence in each group in boys’ group is independent of the prevalence in the girls’ group. These two samples have the same sample of 11; however, the other descriptive statistics are different.

The report is an interpretation of statistical analysis deduced from the descriptive and inferential statistics of the two samples of 11 age groups of boys and girls regarding their obesity prevalence. The analysis incorporates the procedures of hypothesis testing and confidence interval.

Statistical Analysis

The sample means standard deviation, variance, standard error and sum of squares of obesity prevalence for boys are 15.3, 1.672178764, 5.545989542, 1.672178764 and 2882.57 respectively. The mean, standard deviation, variance, standard error and sum of squares of obesity prevalence for girls are 13.681818, 4.858151538, 23.60163636, 1.464787802 and 2295.13 respectively. In the the most appropriate statistical test is t- test for the mean. This is because the variances for the populations from the samples are randomly drawn are unknown. In this regard, the sampling distribution is t–distribution, and therefore, computation of the t- statistic will be consistent with this sampling distribution.

Our hypothesis would test the claim that there is a difference in the obesity prevalence for the different ages groups between boys’ and girls’ group. Thus, the null and alternative hypotheses are;

H0: B-G =0; There is no significant difference in the obesity prevalence between boys’ and girls’ group

H1; B-G ≠0; There is a significant difference in the obesity prevalence between males’ and girls’ group.

Here, B-G = B - G, where, B is the population means of boys, and G is the population means of girls.

In the null hypothesis, we assume the B and G are equal and thus the difference is zero. Apparently, this is a two tailed test. A two tailed test is a hypothesis test whereby the critical region involves areas at the both ends of the sampling distribution of the test statistic. That is H1 ≠ t, t is any statistic. The kind of test, either one tailed or two tailed influences the value of critical value

To compute the test statistic, we employ the formula;

But , est.iM-M

Where ,

s2p = (2882.57+2295.13)/ 20 = 258.885.

est.iM-M =sqrt.(258.885/11+258.885/11) =6.860757976.

±t-test statistic = 1.61818182/6.860757976=±0.235860528

t-test statistic=0.2359 (4 d.p)

The degrees of freedom is 20, that is (11-1) + (11-1). Α= 0.050, α/2 = 0.025

The critical values;

±t (nB – nG -2, α/2)= ±t (20, 0.25)= ±2.086,( from student t- distribution table )

The p- value is 0.8158909, ( read from online p- value calculator for t-test .

The decision rule is to reject the null hypothesis if p- value is less than or equal to the alpha level, α=0.5.Otherwise we fail to reject it .In these case , the p- value is greater than the alpha , so we fail to reject the null hypothesis. Therefore, we can conclude there is enough evidence in the data to support the claim that there is no significant difference in obesity prevalence between the boys and girls in each different age groups.

For this sampling distribution, the estimated standard deviation is 6.860757976 and we can use this to find the margin error .Margin error is computed using the formula; margin error = critical value* standard deviation. In this case the margin error is 13.44708563, (2.086*6.860757976). The 95% confidence intervals for boys’ and girls’ group are (12.02252962, 18.57747) and (10.81083409 ,16.552802).

Conclusion

From the analysis, we can deduce that the boys’ group has higher mean and variation in obesity prevalence as compared to the girls’ group. Also, we can conclude that there is a significant difference in obesity prevalence between the boys and girls.

References

Retrieved on 26th February, 2017 from; http://vassarstats.net/textbook/ch11pt1.html