Hypothesis is a guess or proposition that seeks to explain about a natural phenomenon about population of interest, and it is subject to be tested in a bid to identify the truth or false behind it. In other words, the validity of the proposition has to be determined through definition of both the null and alternative hypotheses. In this case, the entire research or experiment revolves around the null hypothesis. However, a single research may wish to test more than one null hypothesis.

It has to be noted that the researcher tries to disapprove, nullify, or reject the nul

Healthcare Statistics - Introduction to Hypothesis Testing (SLP)

Hypothesis is a guess or proposition that seeks to explain about a natural phenomenon about population of interest, and it is subject to be tested in a bid to identify the truth or false behind it. In other words, the validity of the proposition has to be determined through definition of both the null and alternative hypotheses. In this case, the entire research or experiment revolves around the null hypothesis. However, a single research may wish to test more than one null hypothesis.

It has to be noted that the researcher tries to disapprove, nullify, or reject the null hypothesis, but not the alternative hypothesis. The principle behind the setting of hypotheses is the bid by the researcher to challenge certain population parameters. While defining the hypotheses, H_{0 }is used to denote the null hypothesis while H_{a }is used to denote alternative hypothesis. Basically, while defining the null hypothesis, the researcher must state a certain population parameter is equal to the claimed value. For example, the researcher may claim that the population’s mean height is equal to a certain value, say 130cm. Therefore, the null hypothesis may be stated in form of statement or in form symbols as follows (Rumsey, 2010).

H_{0}: The population mean is equal to 130 or H_{0}: µ = 130, where µ is the population mean.

On the other hand, before conducting hypothesis testing, there are other possible hypotheses that may actually be realized in reality after the researcher has analyzed the data to prove their earlier propositions (null hypotheses). One of the other possible hypotheses is regarded as alternative hypothesis. However, the case for alternative hypothesis is different from that of null hypothesis since the population parameter may be not equal to, less than, or greater than the claimed value. As such, it is the task of the researcher to determine the direction to take while stating the alternative hypothesis depending on the need of the research (Psychology.ucdavis.edu, 2015). For example, from the previously described scenario, the researcher may state the alternative as; H_{a }: The population mean height is not equal to 130cm or the population mean height is greater than 130cm or the population mean height is less than 130cm. Symbolically, the researcher may state the alternative hypothesis as; H_{a}: µ ≠ 130 or H_{a}: µ >130 or H_{a}: µ < 130.

From the given data regarding adults in American who had either been tested or not tested for HIV, the hypotheses may be stated in regard to the proportion of the adults who have not been tested for HIV. Therefore, the null hypothesis would be stated as; H_{0 }: The probability of selecting American adult who has not been tested for HIV is 0.5 or H_{0}: P_{n} = 0.5. On the other hand, the alternative hypothesis can be stated as; H_{a }: The probability of selecting American who has never been tested for HIV is not equal to 0.5 or H_{a}: P_{n} ≠ 0.5. In this case, the researcher may wish to test the hypotheses;

H_{0}: P_{n} = 0.5 versus H_{a}: P_{n} ≠ 0.5, where P_{n }is the probability of selecting American who has never been tested for HIV.

**Question 2**

To test the above hypotheses, one can only use two-tailed test since the deviations of the estimated parameter (0.5) takes more than one direction, equal to, greater than, or less than. This is the key reason as to why the hypotheses was stated in a way that it will allow for considerations of both extremes of the distribution. In addition, the hypotheses stated were selected since it would be used for comparison purposes since there are two samples, American adults who have been tested for HIV and American adults who have not been tested for HIV. One may be interested in knowing if there is any significance relationship between the number of American adults who have tested for HIV and American adults who have never tested for HIV. However, to carry out two-tailed test, there are parameters that need to be computed from both samples. For effective and reliable results, the elements included in the samples should be selected randomly. Otherwise, the results yielded may be biased and misleading. In addition, the computation of the t-value from a specified formula has to be computed so that it may be compared to the critical value read from the Student’s t-table. If the evidence from the analyzed data and the computed statistics reveals that the P_{n }is different from the 0.5, the null hypothesis is rejected and considers the alternative hypothesis. On the other hand, if the computed statistics and data analysis reveal that the P_{n }is equal to 0.5, the null hypothesis is not rejected. Importantly, one should note that in hypotheses testing; both the null and alternative hypotheses are not accepted. Statisticians talk of rejecting and failing to reject the null hypotheses. Depending on the outcome of the test, the researcher is able to make concrete conclusions regarding the data (Moye, 2002).

l hypothesis, but not the alternative hypothesis. The principle behind the setting of hypotheses is the bid by the researcher to challenge certain population parameters. While defining the hypotheses, H_{0 }is used to denote the null hypothesis while H_{a }is used to denote alternative hypothesis. Basically, while defining the null hypothesis, the researcher must state a certain population parameter is equal to the claimed value. For example, the researcher may claim that the population’s mean height is equal to a certain value, say 130cm. Therefore, the null hypothesis may be stated in form of statement or in form symbols as follows (Rumsey, 2010).

H_{0}: The population mean is equal to 130 or H_{0}: µ = 130, where µ is the population mean.

On the other hand, before conducting hypothesis testing, there are other possible hypotheses that may actually be realized in reality after the researcher has analyzed the data to prove their earlier propositions (null hypotheses). One of the other possible hypotheses is regarded as alternative hypothesis. However, the case for alternative hypothesis is different from that of null hypothesis since the population parameter may be not equal to, less than, or greater than the claimed value. As such, it is the task of the researcher to determine the direction to take while stating the alternative hypothesis depending on the need of the research (Psychology.ucdavis.edu, 2015). For example, from the previously described scenario, the researcher may state the alternative as; H_{a }: The population mean height is not equal to 130cm or the population mean height is greater than 130cm or the population mean height is less than 130cm. Symbolically, the researcher may state the alternative hypothesis as; H_{a}: µ ≠ 130 or H_{a}: µ >130 or H_{a}: µ < 130.

From the given data regarding adults in American who had either been tested or not tested for HIV, the hypotheses may be stated in regard to the proportion of the adults who have not been tested for HIV. Therefore, the null hypothesis would be stated as; H_{0 }: The probability of selecting American adult who has not been tested for HIV is 0.5 or H_{0}: P_{n} = 0.5. On the other hand, the alternative hypothesis can be stated as; H_{a }: The probability of selecting American who has never been tested for HIV is not equal to 0.5 or H_{a}: P_{n} ≠ 0.5. In this case, the researcher may wish to test the hypotheses;

H_{0}: P_{n} = 0.5 versus H_{a}: P_{n} ≠ 0.5, where P_{n }is the probability of selecting American who has never been tested for HIV.

**Question 2**

To test the above hypotheses, one can only use two-tailed test since the deviations of the estimated parameter (0.5) takes more than one direction, equal to, greater than, or less than. This is the key reason as to why the hypotheses was stated in a way that it will allow for considerations of both extremes of the distribution. In addition, the hypotheses stated were selected since it would be used for comparison purposes since there are two samples, American adults who have been tested for HIV and American adults who have not been tested for HIV. One may be interested in knowing if there is any significance relationship between the number of American adults who have tested for HIV and American adults who have never tested for HIV. However, to carry out two-tailed test, there are parameters that need to be computed from both samples. For effective and reliable results, the elements included in the samples should be selected randomly. Otherwise, the results yielded may be biased and misleading. In addition, the computation of the t-value from a specified formula has to be computed so that it may be compared to the critical value read from the Student’s t-table. If the evidence from the analyzed data and the computed statistics reveals that the P_{n }is different from the 0.5, the null hypothesis is rejected and considers the alternative hypothesis. On the other hand, if the computed statistics and data analysis reveal that the P_{n }is equal to 0.5, the null hypothesis is not rejected. Importantly, one should note that in hypotheses testing; both the null and alternative hypotheses are not accepted. Statisticians talk of rejecting and failing to reject the null hypotheses. Depending on the outcome of the test, the researcher is able to make concrete conclusions regarding the data (Moye, 2002).