Among 157 African-American men, the mean systolic blood pressure was 146 mm
Hg with a standard deviation of 27. We wish to know if on the basis of these data,
we may conclude that the mean systolic blood pressure for a population of African-
American is greater than 140.
• Setup the null and alternate hypothesis (1 mark)
• Determine the type of the test (1 mark)
• Use α=0.01, conduct the test and accept or reject the hypothesis on the basis of
the test. (Given Z_0.99=2.33) (3 marks)
The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is and the critical value for a right-tailed test is
The rejection region for this right-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value for right-tailed, degrees of freedom, is and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean
is greater than 140, at the significance level.
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