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 μ . Given a P ‑value between 0.01 and 0.05, what conclusion should you draw at the 5% level of significance? No conclusion can be drawn without knowing the exact P ‑value. Accept the null hypothesis, because the P ‑value is less than the level of significance. Reject the null hypothesis, because the P ‑value is less than the level of significance. Fail to reject the null hypothesis, because the P ‑value is less than the level of significance.

Answer 1

a).hypothesis:-

given data are:-

sample mean () = 143

sample sd (s) = 21

sample size (n) = 28

test statistic be:-

df = (n-1) = (28-1) = 27

p value :-

= P(t < -1.764)

= 0.0445 [ in any blank cell of excel type =T.DIST(-1.764,27,TRUE) press enter]

decision:-

p value = 0.0445 < 0.05 (alpha)

so, we reject the null hypothesis and conclude that,there is some evidence that the diet is effective in meeting the target at 0.05 level of significance.

b).DECISION BASED ON P VALUE MENTIONED IN QUESTION:-

given that,

0.01 < p value <0.05

decision:-

p value <0.05 (alpha)

so, we reject the null hypothesis.

the correct option be:-

Reject the null hypothesis, because the P ‑value is less than the level of significance.

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