A Comparison of Descriptive and Differential Statistics

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The aim of this paper is to give a broad understanding of the underlying concepts of quantitative methods as well as offering a feedback on the understanding of the same concepts.

Question 1.

My results differ with those learnt in class because of the error rate which might arise due to the choice of the significance level, the sampling methods can lead to variations in the results. The error rate is caused especially when the null hypothesis is accepted based on the critical area due to the wrong or smaller choice of the significance level.

Question 3.

a. The sample median is an unbiased estimator of the population median if the distribution of the population is normal. On the other hand, the sample mean is an unbiased estimator of the population median if the population is not symmetric. More importantly, the sample mean will never be a biased estimator of the population mean unless there are sampling errors only. In this case, the non-sampling errors entails among others, poor designing of the questionnaires, biasness in selection, and target population not being equivalent to the sampled population.

b. From the results in questions 1 and 2 above, the sample mean and the sample median are unbiased estimators of the population mean. The values are equal and the population is normally distributed.

c. A consistent estimator implies that there are insignificant errors as the sample size grow larger. In our case, based on the above results, the sample mean is a consistent estimate of the population mean. This implies that the probability that the errors will vary more than a given value extends to zero as the sample size increases.

d. An efficient estimator has the smallest possible variance. From the results above, the median is the best estimator.

Question 4.

a. We use high levels of 0.10 or 0.15

The significance level is the probability of rejecting the null hypothesis when it is true. The choice of a higher level of significance tries to avoid the error rate which is majorly associated with the acceptance of the null hypothesis since it falls within the critical region. Higher levels provide a wider region.

b. The histogram shows that the data is normally distributed and that the central values can be used to explain the data set appropriately.

c. The comparison between descriptive mean gives the same value as that for differential statistics.

d. Captured in the excel….

January 19, 2024
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