Introduction to Hypothesis Testing

**QUESTION**

the Session Long Project, write a (2-3 pages) paper in which you:

Develop a null hypothesis and an alternative hypothesis based on the data you have collected.

Discuss why you have chosen the hypotheses you developed above. Be sure to discuss the concept of null hypothesis in your response.

Introduction to Hypothesis Testing

**ANSWER**

Introduction to Hypothesis Testing

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Develop a null hypothesis and an alternative hypothesis based on the data you have collected.

The following is the data I have collected, consisting of the sample mean, sample standard deviation, and the sample size; Sample mean, x̄ = 152, Sample standard deviation, s = 16.1, and Sample size, n = 5. I intend to use the Z test to test the hypothesis for this data. The following statement represents the null hypothesis;

H0: µ = 5

The z value obtained is 20.42. Therefore we fail to reject the null hypothesis. A z value of 20.42 lies within the area of non-rejection. The point of cutoff 4.604. Any z value that is greater than this cutoff of 4.604 will be accepted. Therefore, since 20.42 is bigger than 4.604, I will accept the hypothesis, H0: µ = 5, the null hypothesis.

The following is the data I have collected, consisting of the sample mean, sample standard deviation, and the sample size; Sample mean, x̄ = 83.2, Sample standard deviation, s = 65.2, and Sample size, n = 5. The following statement represents the alternative hypothesis;

H1: µ ≤ 5

The z value obtained from this test was 2.68. Therefore, since the z score value of 2.68 lies in the area of rejection, I will fail to accept the null hypothesis. In this case, the point of cutoff is 4.604. Therefore, any z value that is not greater than 4.604 should be not be accepted. Since 4.604, which is the cutoff value, is greater than the z value of 2.68, I fail to accept the null hypothesis.

Discuss why you have chosen the hypotheses you developed above. Be sure to discuss the concept of the null hypothesis in your response.

A hypothesis is associated with two kinds of statements: the alternative hypothesis and the null hypothesis. The easiest definition of null would be to define it as the antonym of an alternative hypothesis. When it comes to the null hypothesis, a researcher’s goal is to reject, nullify, or disprove. The null hypothesis often represents a common and general view of a phenomenon. In contrast, the alternative hypothesis represents what the person doing research thinks could cause or reason for a scenario.

Statistical implication begins with identifying that study questions can be formulated in the conditions following a choice between a pair of mutual and clear options. Null hypothesis statement represents the meaning that scenarios are equal to each other, as in, they are not different from the theoretical expectation. An alternative hypothesis means that scenarios are not equal to each other, as in, they are diverse from the theoretical expectation. (McDonald, 2014).

The data that I used above was from a blood pressure monitoring activity run for five consecutive days, which belonged to a Black American woman aged 52 years. The aim was to prove whether the propositions that were hypothesized were correct by testing the outcomes. As much as these variable discoveries are not easy to elaborate on a genetic foundation, they, however, cannot be taken into account for by the diversities in the significant environmental peril factors of hypertension, for instance, salt intake and obesity now that these factors have been managed, and in various researches that have exposed an ethnic diversity in blood pressure. (Pickering, T. G., 2001).

The null hypothesis, in this case, was Ho: the duration spent to monitor the blood pressure for five consecutive days was not rejected and showed no diversity in comparison to the blood pressure monitoring while there existed a diversity in monitoring. This is referred to as a false negative, “beta” error, or type II error.

The alternative hypothesis, in this case, was H1: the duration spent to monitor blood pressure for five consecutive days was not accepted, and had diversity on the level where an outcome was rendered significant, and this is referred to as type I error, which is often indicated by alpha (Wilcox, 2017).

The null hypothesis proves that a relationship existed between the variable that was being monitored. Therefore, the alternative hypothesis proved that there did not exist any relationship. Once you accept the null hypothesis, then the alternative hypothesis cannot be accepted. If you reject the null hypothesis and it is true, then in this case, a Type I error occurs, but if the null hypothesis is not true, then a Type II error occurs. A p-value is used to establish the degree of evidence of a hypothesis, and when there is evident statistical significance, the research outcome is deemed dependable.

Often, hypothesis testing goes along with the evaluation of whether or not to accept the null hypothesis. More so, it is related to statistical methods that focus on establishing whether to reject or accept the hypothesis. After establishing the null and alternative hypothesis, it gets much easier to proceed with hypothesis testing by comparing data collected about blood pressure monitoring. Finally, the test statistic is often useful to evaluate the authenticity compared to an obtained critical value, which helps to decide whether you reject or accept the null hypothesis (Wilcox, 2017).

References

McDonald, J.H., (2014). Basic Concepts of Hypothesis Testing. Handbook of Biological

Statistics. 3rd. Ed. Sparky House Publishing, Baltimore, MD. Retrieved from:

http://www.biostathandbook.com/hypothesistesting.html.

Pickering, Thomas G, MD, DPhil. (2001). Why Is Hypertension More Common in African

Americans? Medscape. Retrieved from: http://www.medscape.com/viewarticle/407721.

Wilcox, R. R. (2017). Introduction to robust estimation and hypothesis testing.