Suppose a researcher is interested in the relationship between periodontal disea

Question

Suppose a researcher is interested in the relationship between periodontal disease and a number of negative health outcomes. One outcome of particular interest to the researcher is hypertension (assume defined as systolic blood pressure above 140 mmHG). Suppose a team gathers a SRS of 348 participants with periodontal disease, and finds the sample average systolic blood pressure to be 157 mmHG. Using an assumed sigma=16 mmHG, conduct a 1 sample Z test to determine if there is a relationship between periodontal disease and hypertension in this population. (Use alpha=0.05) What should you do based upon information provided? A. Reject the Ho B. Fail to reject the Ho C. All of the above D. None of the above

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 140
Alternative hypothesis: 140

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)
S.E = 0.8577
z = (x - ) / SE
z = 19.82

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than - 19.82 or greater than 19.82.

Thus, the P-value = Less than 0.00001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

Reject the H0.

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