4. It is known that individuals in a particular population have probability q = 0.45 of having high blood pressure. (And so the probability of individuals in this population having low blood pressure is 1-q = 0.55.) A researcher strongly suspects that regular exercise is positively related to lower blood pressure, and so tests the blood pressure in a sample of 20 individuals from this population known to exercise more than 12 hours per week. (i) The null hypothesis for this experiment is that there is no relationship between regular exercise and blood pressure. State this null hypothesis in terms of the parameter q. (ii) State an appropriate alternative hypothesis, also using the parameter q, that reflects the suspicion that regular exercise is positively related to lower blood pressure. (iii) Now suppose that exactly 2 of the individuals in the sample have high blood pressure. To apply a one-tailed test to determine the p-value, calculate the probability p of 2 or fewer individuals out of 20 having low blood pressure if the null hypothesis is in effect. (Assume that the number of individuals in the sample having high blood pressure is binomially distributed.) (iv) Use the value of p you found in (iii) to determine the significance of the data, using the same criteria as in the preceding problem.
4. It is known that individuals in a particular population have
q = 0.45 of having high blood pressure. (And so the probability of
individuals in this population having low blood pressure is 1-q = 0.55.) A
researcher strongly suspects that regular exercise is positively related to
lower blood pressure, and so tests the blood pressure in a sample of 20
individuals from this population known to exercise more than 12 hours per
week.
(i) The null hypothesis for this experiment is that there is no
relationship between regular exercise and blood pressure. State this null
hypothesis in terms of the parameter q.
(ii) State an appropriate alternative hypothesis, also using the parameter
q, that reflects the suspicion that regular exercise is positively related
to lower blood pressure.
(iii) Now suppose that exactly 2 of the individuals in the sample have
high blood pressure. To apply a one-tailed test to determine the p-value,
calculate the probability p of 2 or fewer individuals out of 20 having
low blood pressure if the null hypothesis is in effect. (Assume that the
number of individuals in the sample having high blood pressure is binomially
distributed.)
(iv) Use the value of p you found in (iii) to determine the significance
of the data, using the same criteria as in the preceding problem.
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