determine the probability that the null hypothesis is falsely rejected
Running head: STATISTICS 1
Case 4: Drawing Inferences about Population Means and Proportions
Hypotheses Testing Procedure
The testing procedure is used to find out if the hypothesis statement should be rejected or accepted. The first step is to state the null hypothesis and the alternative hypothesis. After stating, the second step involves selecting the test statistics and the required level of significance. Then the decision rules are stated to the null should be accepted or rejected. This involves determining the critical value or the level of significance. The critical value is used to divide the accepted from the non-accepted region. After stating the decision rules, the fourth .step involves computing the test and making the decision after comparing the calculated test statistics with the critical value. If the calculated value is within the non-acceptable region (s), the H0 should be rejected. Finally, the decision is made based on the computed test statistic.
Null and Alternative Hypotheses
The null hypothesis assumes that cholesterol treatment does not have any effect on the participant. On the other hand, the alternative hypothesis tests whether cholesterol treatment has any effect on the cholesterol level on the participant. The null hypothesis (H0): Treatment does not reduce the cholesterol level in human body. The null hypothesis assumes that there is no relationship between the increase/decrease in the cholesterol level. The alternative hypothesis (H1) can be formulated as follows: Treatment reduces cholesterol level in human body. In this case, the alternative hypothesis tests whether treatment can minimize the cholesterol level according to the collected data (Cook, Netuveli, & Sheikh, 2004).
I will apply the chi-square test to evaluate the effectiveness of the cholesterol test on the participants. The chi test formula can be presented as, where k= predetermined degree of freedom, g= observed value, and E= the expected number of individuals.” The formula shows the relationship between the treatment and no treatment for cholesterol. Also, the test provides a single value to represent the two different variables (the treatment and the expected). The chi test values can be calculated as shown below:
|Cholesterol Decreased||No Cholesterol Decrease||Total|
|Treatment||= 33.40||= 18||56|
|No treatment||= 34.60||= 28||58|
Calculating the P-Value
According to Norman and Streiner (2014), “P-value is used to determine the probability that the null hypothesis is falsely rejected.” Both z-scores and p-values are associated with the normal distribution. The P-value can be used to determine the “likely” or “unlikely” of the impact of treatment on the level of cholesterol (assuming the null hypothesis is true). On the other hand, when the p-value is small, the null hypothesis is rejected. On the other hand, According to Norman, and Streiner (2014), ‘P-value is greater than the required significance level, the H0 is not rejected” Finally, the degrees of freedom are determined using the following formula: (Rows – 1) x (columns – 1) = 1.
Therefore, the p-value = 0.075
There is no Enough Evidence
According to Norman, & Streiner (2014), “A small p-value indicates a large variation which means that there is a large difference between the observed and the expected data.” This means that the observed vary from the expected if the treatment does not improve the condition. On the other hand, a small p-value of 0.0750 means that there is there is enough evidence to conclude that the treatment is effective. The results mean that cholesterol treatment is effective which provide a basis to reject the null hypothesis (Norman, & Streiner, 2014).
Cook A., Netuveli, G., & Sheikh, A. (2004). Basic skills in statistics: A guide for healthcare professionals. London, GBR: Class Publishing. eISBN: 9781859591291.
Norman, G. R., & Streiner, D. L. (2014).Biostatistics: The Bare Essentials [4th ed., e-Book]. Shelton, Connecticut: PMPH-USA, Ltd. eISBN-13: 978-1-60795-279-4