A researcher is investigating the effectiveness of a new medication for lowering

Question

A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores average =160 with a standard deviation of =20. The researcher selects a sample of 100 individuals and measures their systolic blood pressure after they take the medication for 60 days. The researcher finds that the average systolic blood pressure for the sample is 155. Using a z-test with an alpha of 0.05, two-tailed, is there enough evidence to support that this drug is effective? Make sure to run an entire hypothesis test.

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

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

Null hypothesis: = 160
Alternative hypothesis: 160

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the z - test statistic (z).

DF = n - 1 = 100 - 1 = 99
z = (x - ) / ( / sqrt(n)) = (155 - 160)/(20/sqrt(100)) = -5/2 = -2.5

Since we have a two-tailed test, the P-value is the probability that the z statistic having 99 degrees of freedom is less than -2.5 or greater than 2.5.

We use the z Distribution Calculator to find P(z < -2.5), and P(z > 2.5)

The P-Value is 0.012419.
The result is significant at p < 0.05

Interpret results. Since the P-value (0.012) is less than the significance level (0.05), we cannot accept the null hypothesis.We have enough evidence to support that this drug is effective.

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