Table of Contents

- Hypothesis Analysis Descriptive Analysis And Confidence Interval Determination Of Novel Drug For Cholesterol Level Reduction And Its Effect On Plasma Cholesterol Levels Assignment
- 1.0 Definition of the null and alternatives hypothesis
- 2.0 Methodology
- Z-Test Two-Sample Assuming Unequal Variances
- The descriptive statistics of post-treatment time on volunteers

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In a set of given single observed variables, no statistical significance and relationship are present in terms of typical statistical theory. This is known in the name of the null hypothesis between two sets of measured phenomena and observed data.

In a hypothesis test when one of two mutually exclusive hypotheses is chosen that is known in the name of the alternative hypothesis. To a specified value population parameter when the value does not get equal it is known in the name of the alternative hypothesis. The value that is associated with no effect is known in the name of the alternative hypothesis.

The methodologies that are used in this discussion is a confidence interval, descriptive statistics, Z-test assuming equal variances of two sample, samples for means Z-test paired two, Z-test for two assuming unequal variances samples (Michel, *et al**. *2020).

Between a pair of values around the mean regarding the parameter of it, a confidence interval displays the probability. In a method sampling degree of uncertainty, uncertainty is measured through intervals of confidence. 95% or 99% of the confidence level is most often constructed (Shultz, 2018).

Regarding sample of the population or entire population, it will represent. Into measures of central tendency, descriptive statistics are broken with measures of variability (Diaz, 2020).

To determine the null hypothesis will be accepted or not it is determined through Z-test paired Two-Sample for Means in terms of two sample students Z-test. Over here it is done on the volunteers (Bhatnagar, *et al**.* 2021). The variance of both populations is equal this test does not assume that. The difference between the two means is computed in terms of standard error (McShane, *et al**. *2019). Z-ratio in terms of unequal variance is calculated by dividing two sample means difference with standards error of the difference between two means. After that calculation of Df is done (Gigerenzer, 2018).

For the equality of the two means, the Z-test provides an exact test. It is done for the normal population with the unknown, variances with equal values (Amrhein,* et al.* 2019).

**3.0 Results**

** Confidence interval of the pre-treatment value**

(Source: self-created in MS Excel)

The calculation is done regarding the confidence of the pre-treatment value. The values of the mean sample standard deviation sample, size of the sample, window C.I, upper limit, the lower limit are calculated over here. At last final interpretation is given is done. The value of the sample means is derived £15.743, the value of sample standard deviation is derived £14.18949857, the sample size is 100, the value of window C.I. is derived £2.333964819, the upper limit is derived £18.07696482, and the lower limit is derived £13.40903518. Between £13.40903518 and £18.07696482 is given.

** Confidence interval of post-treatment value**

(Source: Self-created in MS Excel)

The calculation is done regarding the confidence interval of the post-treatment value. Regarding it, values are derived regarding a sample mean, sample standard deviation, sample size, window c.i, upper limit, and lower limit. The value of the sample means is £15.723, sample standard deviation value is £14.20364767. The sample size value is 100, window C.i. value is £2.336292138. The value of the upper limit is derived £18.05929214. The value of the lower limit is derived £13.38670786.

** Two-Sample for Means Z-Test Paired**

(Source: In MS Excel self-created)

The above calculation is done in terms of Z-Test paired two samples for Means. The value of mean is £5.986 for pre-treatment, the value of the variance of pre-treatment is £0.008983673, and the observation is done on 50 volunteers. The values that are calculated above have changed depending on the Z-test process.

** Assuming Equal Variances Z-Test Two-Sample**

(Source: In MS Excel Self Created)

The value of the mean pre-treatment time is £5.986 and for post-treatment time is £5.946. The value of the variance of pre-treatment time is £0.008983673 and for post-treatment time is £0.02335102. The observation is on 50 volunteers in this Z-Test Two-Sample Assuming Equal Variances. The other values changes according to the nature Z-Test process.

(Source: In MS Excel Self Created)

The above calculation is done regarding Assuming Unequal Variances Z-Test Two-Sample. The value of the mean of pre-treatment time is £5.986 and of post-treatment time is £5.946. The value of the variance of pre-treatment time is £0.008983673 and of post-treatment time is £0.02335102. The above observation is done on 50 volunteers in both pre-treatment and post-treatment processes.

(Source: In MS Excel Self-created)

The descriptive statistics are done for post-treatment time on volunteers. The value of the mean, standard error, median, mode, range, minimum, maximum, sum, count, largest, and smallest values are the same. But the value of standard deviation, sample variance, Kurtosis, and skewness change according to the largest and smallest number orders are arranged.

For the cholesterol-lowering properties a novel drug was tested and on 50 volunteers experiment is carried out. In terms of pre-treatment value, plasma cholesterol concentrations were measured. Once a month drugs were given to these volunteers. The measurement was again done for plasma cholesterol concentration.

From the above discussion and calculation, it is determined that at a 95% level of confidence have very much evidence to disprove this assumption.

The above methods are used to determine the values of pre-treatment and post-treatment values of a novel drug for cholesterol-lowering properties and a significant effect on plasma cholesterol levels.

**4.0 Conclusion**

From the above discussion, it is concluded that confidence interval, two samples for means Z-Test paired, assuming equal variances Z-test two Sample, assuming unequal variances Z-Test two-sample and descriptive statistics are the major processes for deriving significant effect on plasma cholesterol levels. The ranking system that is calculated in this topic through it is determined the effect of cholesterol levels on every volunteer those have participated after drugs are given to those volunteers. That is the reason proper allocation is very much important in every aspect of calculated values is very much important to derive the proper result of the test.

**Reference list**

**Journal **

Amrhein, V., Greenland, S. and McShane, B., 2019. Scientists rise up against statistical significance.

Amrhein, V., Trafimow, D. and Greenland, S., 2019. Inferential statistics as descriptive statistics: There is no replication crisis if we don’t expect replication. *The American Statistician*, *73*(sup1), pp.262-270.

Bhatnagar, V., Poonia, R.C., Nagar, P., Kumar, S., Singh, V., Raja, L. and Dass, P., 2021. Descriptive analysis of COVID-19 patients in the context of India. *Journal of Interdisciplinary Mathematics*, *24*(3), pp.489-504.

Blose, N.J., 2021. *Descriptive analysis of routine childhood immunisation timelines in the Western Cape, South Africa* (Master's thesis, Faculty of Health Sciences).

Bothwell, L.E., Avorn, J., Khan, N.F. and Kesselheim, A.S., 2018. Adaptive design clinical trials: a review of the literature and ClinicalTrials. gov. *BMJ open*, *8*(2), p.e018320.

Brossart, D.F., Laird, V.C. and Armstrong, T.W., 2018. Interpreting Kendall’s Tau and Tau-U for single-case experimental designs. *Cogent Psychology*, *5*(1), p.1518687.

Bzdok, D. and Ioannidis, J.P., 2019. Exploration, inference, and prediction in neuroscience and biomedicine. *Trends in neurosciences*, *42*(4), pp.251-262.

Diaz, J.H., 2020. Hypothesis: angiotensin-converting enzyme inhibitors and angiotensin receptor blockers may increase the risk of severe COVID-19. *Journal of travel medicine*.

Emmert-Streib, F. and Dehmer, M., 2018. A machine learning perspective on Personalized Medicine: an automized, comprehensive knowledge base with ontology for pattern recognition. *Machine Learning and Knowledge Extraction*, *1*(1), pp.149-156.

Gigerenzer, G., 2018. Statistical rituals: The replication delusion and how we got there. *Advances in Methods and Practices in Psychological Science*, *1*(2), pp.198-218.

Gysi, D.M., Do Valle, Í., Zitnik, M., Ameli, A., Gan, X., Varol, O., Ghiassian, S.D., Patten, J.J., Davey, R.A., Loscalzo, J. and Barabási, A.L., 2021. Network medicine framework for identifying drug-repurposing opportunities for COVID-19. *Proceedings of the National Academy of Sciences*, *118*(19).

Ho, J., Tumkaya, T., Aryal, S., Choi, H. and Claridge-Chang, A., 2019. Moving beyond P values: data analysis with estimation graphics. *Nature methods*, *16*(7), pp.565-566.

McShane, B.B., Gal, D., Gelman, A., Robert, C. and Tackett, J.L., 2019. Abandon statistical significance. *The American Statistician*, *73*(sup1), pp.235-245.

Michel, M.C., Murphy, T.J. and Motulsky, H.J., 2020. New author guidelines for displaying data and reporting data analysis and statistical methods in experimental biology. *Journal of Pharmacology and Experimental Therapeutics*, *372*(1), pp.136-147.

Moore, N., Berdaï, D., Blin, P. and Droz, C., 2019. Pharmacovigilance–The next chapter. *Therapies*, *74*(6), pp.557-567.

Shultz, M.D., 2018. Two decades under the influence of the rule of five and the changing properties of approved oral drugs: miniperspective. *Journal of medicinal chemistry*, *62*(4), pp.1701-1714.

Thomford, N.E., Senthebane, D.A., Rowe, A., Munro, D., Seele, P., Maroyi, A. and Dzobo, K., 2018. Natural products for drug discovery in the 21st century: innovations for novel drug discovery. *International journal of molecular sciences*, *19*(6), p.1578.

Varpio, L., Paradis, E., Uijtdehaage, S. and Young, M., 2020. The distinctions between theory, theoretical framework, and conceptual framework. *Academic Medicine*, *95*(7), pp.989-994.

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