A special diet is intended to reduce systolic blood pressure

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 = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean . Given a P-value between 0.01 and 0.05, what conclusion should you draw at the 5% level of significance?

A. Fail to reject the null hypothesis because the P-value is less than the level of significance.

B. Reject the null hypothesis because the P-value is less than the level of significance.

C. Accept 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.

Solution

Set Up Hypothesis
Null, H0: U>=150
Alternate, H1: U<150
Test Statistic
Population Mean(U)=150
Sample X(Mean)=143
Standard Deviation(S.D)=21
Number (n)=28
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =143-150/(21/Sqrt(27))
to =-1.764
| to | =1.764
Critical Value
The Value of |t | with n-1 = 27 d.f is 1.703
We got |to| =1.764 & | t | =1.703
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -1.7638 ) = 0.04454
Hence Value of P0.05 > 0.04454,Here we Reject Ho

ANS:
B. Reject the null hypothesis because the P-value is less than the level of significance.