A special diet is intended to reduce systolic blood pressure. If the diet is eff

Question

A special diet is intended to reduce systolic blood pressure. 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 with high blood pressure had an average cholesterol 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 cholesterol for patients in this group is approximately Normal with mean . The P-value for the one-sample t test is

Explanation / Answer

Solution:-

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

Null hypothesis: > 150

Alternative hypothesis: < 150

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean 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 = 3.969

DF = n - 1

D.F = 27

t = (x - ) / SE

t = - 1.76

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.

The observed sample mean produced a t statistic test statistic of - 1.76. We use the t Distribution Calculator to find P(t < - 1.76).

Thus the P-value in this analysis is 0.045.

Interpret results. Since the P-value (0.045) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that that the diet is effective in meeting the target.

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