A study looking at symptoms and care-seeking behavior in African-American patients with chest pain, measured the systolic blood pressure of 157 African-American men seen in an emergency department. The mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. The researchers wish to know if on the basis of these data, they can conclude that the mean systolic blood pressure is greater than 140. Use α=.05.  Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic, and 5) your conclusion including a comparison to alpha or the critical value. What do the results mean? You MUST show your work to receive full credit. Partial credit is available.

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Asked Oct 4, 2019
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A study looking at symptoms and care-seeking behavior in African-American patients with chest pain, measured the systolic blood pressure of 157 African-American men seen in an emergency department. The mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. The researchers wish to know if on the basis of these data, they can conclude that the mean systolic blood pressure is greater than 140. Use α=.05. 
 
Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic, and 5) your conclusion including a comparison to alpha or the critical value. What do the results mean? You MUST show your work to receive full credit. Partial credit is available.

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Expert Answer

Step 1

Hypothesis Formulation:

Null Hypothesis generally contains the '=' sign while the alternate hypothesis contains the claim. Here, the claim of the researchers is that the mean systolic BP is greater than 140.

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Ho u140 H 140

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Step 2

Appropriate Test:

As the sample size is large (greater than 30), we'll use Z test.

Step 3

Calculation of test statistic:

The formula for test statistic is given below 

After substituting sample mean = 146, sample standard deviation = 27, n = 157 and µ0=140 we get test stait...

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Z = 146-140 Z 27 V157 Z 2.784436

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