Question

When 14 different second-year medical students measured by the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 15 mmHg, use a 0.05 significance level to test the claim that the mean blood pressure level is less than 140 mmHg. Hyper- tension is defined to be a blood pressure level that is too high because it is 140 mmHg or greater. Assume the blood pressure levels are normally distributed.
132 140 135 130 120 128 128 130 120 144 143 130 140 150

Answer 1

For the given data

mean = 133.5714

The provided sample mean is X = 133.57 and the known population standard deviation is o = 15, and the sample size is n = 14 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: > 140 Hall <140 This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used (2) Rejection Region Based on the information provided the significance level is a = 0.05, and the critical value for a left- tailed test is ze = -1.64 The rejection region for this left-tailed test is R = {2:2<-1.64} (3) Test Statistics The Z-statistic is computed as follows: X-H 2- 3 133.57 - 140 15/V14 -1.604

(4) Decision about the null hypothesis Since it is observed that 2 = -1.604 > Ze = -1.64, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p=0.0544, and since p= 0.0544 > 0.05, it is concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the  mean blood pressure level is less than 140 mmHg  at the 0.05 significance level.