The distribution of diastolic blood pressures for the popula

The distribution of diastolic blood pressures for the population of female diabetics between the ages of 30 and 34 has an unknown mean µ_d and standard deviation ?_d = 9.1 mm Hg.

It may be useful to physicians to know whether the mean of this population is equal to the mean diastolic blood pressure of the general population of females in this age group, 74.4 mm Hg.

(a) What is the null hypothesis of the appropriate test?

(b) What is the alternative hypothesis?

(d) What conclusion do you draw from the results of the test?

(e) Would your conclusion have been different if you had chosen ? =0.01 instead of ? =0.05?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   74.4   [ANSWER, NULL HYPOTHESIS]

b)

Ha:    u   =/   74.4   [ANSWER, ALT HYPOTHESIS]

**************************
              
c)

As we can see, this is a    two   tailed test.      
              
df = n - 1 =    9          
              
Getting the test statistic, as              
              
X = sample mean =    84          
uo = hypothesized mean =    74.4          
n = sample size =    10          
s = standard deviation =    9.1          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.33602918          
              
Also, the p value is              
              
p =    0.008715056   [ANSWER, P VALUE]      

*****************************

d)
              
As P < 0.05, we reject the null hypothesis. There is significant evidence that the mean of diastolic blood pressures for the population of female diabetics is not 74.4 mmHg.  

*******************************

e)

No. P < 0.01 as well, so we keep the same conclusion.