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 ì. Based on the data, the value of the one-sample t statistic is:
xvb
To determine if there is sufficient evidence that the diet is effective in meeting the target, we can use a one-sample t-test.
The one-sample t statistic is calculated using the formula:
t = (sample mean - target mean) / (sample standard deviation / √n)
Given the information provided:
- sample mean = 143
- target mean = 150
- sample standard deviation (s) = 21
- sample size (n) = 28
We can plug these values into the formula to calculate the one-sample t statistic:
t = (143 - 150) / (21 / √28)
Firstly, we need to calculate the value for "√28":
√28 ≈ 5.2915
Now, we can substitute the values into the formula:
t = (143 - 150) / (21 / 5.2915)
t = -7 / 3.969
t ≈ -1.764
Therefore, the value of the one-sample t statistic, based on the given data, is approximately -1.764.