Question

From a nationwide study, we know that the mean diastolic blood pressure is 66.1 mm gH for children aged 5-6 years of age, and that the measurements are normally distributed. Blood pressure measurements were taken on 11 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 60.4 mm Hg with standard deviation 8 mm Hg.

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

Here we have n = 11, $\overline{x}$ = 60.4, s = 8

Claim : Whether the mean diastolic blood pressure is different than 66.1 mm gH for children aged 5-6 years of age.

The hypothesis are :

H0 : $\mu$ = 66.1 v/s H1: $\mu$$\neq$ 66.1

The test statistic is,

t: s/Vn S

60.4 66.1 8/ 11

= -2.363

d)

df = n -1 = 11 -1 =10

p value = 2 * p ( t < -2.363 )

We look in to the t table, in the row of df = 10 we search for t value 2.363, which lies between the two values 2.228 and 2.764. So we found two tailed probabilities across these two values as 0.05 and 0.02 .

So we say that 0.02 < p value < 0.05 or 0.01 < p value < 0.05

e) Here α = 0.05.

So p value < α . Hence we reject null hypothesis.

There is sufficient evidence to support the claim that the mean diastolic blood pressure is different than 66.1 mm gH for children aged 5-6 years of age.