Question

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of x = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean u. Given a P-value between 0.01 and 0.05, what conclusion should you draw at the 5% level of significance? a. Accept the null hypothesis because the P-value is less than the level of significance. b. Fail to reject the null hypothesis because the P-value is less than the level of significance. c. Reject the null hypothesis because the P-value is less than the level of significance d. No conclusion can be drawn without knowing the exact P-value.

Answer 1

At the 5% significance level, since the P-value is between 0.01 and 0.05, it is less than the level of significance of 0.05. Therefore, we reject the null hypothesis and conclude that the special diet is statistically significantly effective in reducing systolic blood pressure among patients with stage 2 hypertension.

Step-by-step explanation:

To determine if the special diet is effective for reducing systolic blood pressure among patients with stage 2 hypertension, we use hypothesis testing. The null hypothesis (H0) would assert that the average systolic blood pressure of this group is 150 or higher even after the diet. The alternative hypothesis (H1) is that the average systolic blood pressure is below 150 after the diet. Given the sample average (x=143) with a standard deviation (s=21) and a sample size of 28 patients, we can perform a one-sample t-test to test the effectiveness of the diet.

The P-value is a measure of the strength of the evidence against the null hypothesis. Since the provided P-value is between 0.01 and 0.05, we compare it with our significance level (α=0.05). Since the P-value is less than α, which implies the P-value provides strong evidence against the null hypothesis, we can reject the null hypothesis. This suggests that there is statistically significant evidence at the 5% level to conclude that the average systolic blood pressure has decreased below 150 due to the diet, indicating its effectiveness.

Answer 2

To determine if the special diet is effective in reducing systolic blood pressure among patients diagnosed with stage 2 hypertension, a hypothesis test needs to be conducted. Without knowing the exact P-value, it is not possible to draw a conclusion.

Step-by-step explanation:

To determine if the special diet is effective in reducing systolic blood pressure among patients diagnosed with stage 2 hypertension, we can conduct a hypothesis test.

H0: The average systolic blood pressure after six months on the diet is greater than or equal to 150.

Ha: The average systolic blood pressure after six months on the diet is less than 150.

Given a P-value between 0.01 and 0.05, we can compare the P-value to the level of significance (α = 0.05) to draw a conclusion.

If the P-value is less than the level of significance, we reject the null hypothesis and conclude that the diet is effective in meeting the target. If the P-value is greater than or equal to the level of significance, we fail to reject the null hypothesis and do not have sufficient evidence to conclude that the diet is effective.

In this case, the student did not provide the exact P-value, so we cannot determine the conclusion without knowing the exact value. Therefore, the correct answer is d. No conclusion can be drawn without knowing the exact P-value.