Answer to Question #126983 in Statistics and Probability for Jackson Maclay

Question

A District Commissioner (DC) is worried about the rising numbers in high blood
pressure related deaths in her district, and she wants to end the problem. A
reputable research officer has claimed that the situation is probably as a result of
the ageing population of the district. Ten hospital patients were sampled from the
district, and their blood pressure (Y) and age (X) were summarized as follows:
Patient 1 2 3 4 5 6 7 8 9 10
Age 20 25 50 30 45 60 10 15 35 70
Blood
pressure
80 85 125 90 100 135 80 70 100 140

Answer 1

solution:

Let age be sample 1 and blood pressure be sample 2

From the given data we have the following sample mean , sd and sample size for each sample.

The provided sample means are shown below:

$\bar X_1$ = 36

$\bar X_2$ = 100.5

Also, the provided sample standard deviations are:

$s_1 = 19.83$

$s_2 = 24.66$

and the sample sizes are $n_1 = 10$

and $n_2 = 10$

The following null and alternative hypotheses need to be tested:.

$Ho: \mu_1 ​ = \mu_2 ​$

$Ha: \mu_1 ​ ≠ \mu_2$

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

t-statistic is computed as follows:

t= $\frac{\overline{X1}-\overline{X2}}{\sqrt{\frac{s1^{2}}{n1}+\frac{s2^{2}}{n2}}}$

=$\frac{36-100.5}{\sqrt{\frac{19.83^{2}}{10}+\frac{24.66^{2}}{10}}}$

=−6.446

Critical value:Based on the information provided, the significance level is 

α=0.05, and the degrees of freedom are df = n1+n2-2= 10+10-2=18

Using t table , it is found that the critical value for this two-tailed test is 

tc​=2.108.

Since it is observed that ∣t∣=6.446>tc=2.108, it is then concluded that the null hypothesis is rejected.

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1 is different than μ2

​, at the 0.05 significance level.