Question

From a nationwide study, we know that the mean diastolic blood pressure is 60 mm gH for children aged 5-6 years of age, and that the measurements are normally distributed. Blood pressure measurements were taken on 13 children aged 5-6 years living in a specific community to determine whether their living conditions resulted in a difference in mean blood pressure. For these children the average diastolic blood pressure was found to be 55 mm Hg with standard deviation 7.5 mm Hg.

a) The null hypothesis for this test will be:
H0: x̄ < 55
H0: μ > 55
H0: x̄ = 60
H0: μ = 60

b) The alternative hypothesis for this test will be:
Ha: x̄ < 55
Ha: μ > 55
Ha: μ ≠ 60
Ha: μ < 60

c) Compute the value of the test statistic. (Give answer to two places past decimal.)

d) Find bounds on the P value for the test.
P < .01
.01 < P < .05
.05 < P < .1
P > .1

e) Is the evidence against H0 strong enough to reject at α = 0.05 ?
Yes, reject H0
No, do not reject H0
Not enough information to decide.

Answer 1

a)

b) We wanted to know whether there is difference in the mean diastolic blood pressure. so a two tailed alternative suits this situation

c)

d) p value is calculated for 12 degrees of freedom and it is 0.0335 which is between 0.01 and 0.05

e) Since p value <0.05 we reject the null hypothesis and we conclude that there is enough evidence from the sample to believe at 5% significance level that there is significant change in the mean diastolic blood pressure