Question #348548

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)

1
Expert's answer
2022-06-07T08:48:48-0400

The following null and alternative hypotheses need to be tested:

H0:μ140H_0:\mu\le140

H1:μ>140H_1:\mu>140

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 α=0.01,\alpha = 0.01, df=n1=156df=n-1=156 and the critical value for a right-tailed test is tc=2.350489.t_c = 2.350489.

The rejection region for this right-tailed test is R={t:t>2.350489}.R = \{t:t>2.350489\}.

The t-statistic is computed as follows:


t=xˉμs/n=14614027/157=2.7844t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{146-140}{27/\sqrt{157}}=2.7844


Since it is observed that t=2.7844>2.350489=tc,t=2.7844>2.350489=t_c, it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for right-tailed, df=156df=156 degrees of freedom, t=2.7844t=2.7844 is p=0.003013,p= 0.003013, and since p=0.003013<0.01=α,p= 0.003013<0.01=\alpha, it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean μ\mu

is greater than 140, at the α=0.01\alpha = 0.01 significance level.



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