Question

In a study designed to test whether there is a difference between the
average heights of adult females born in two different counties, country
A and country B, random samples yielded the following results:
Yielded Values Country A Country B
sample size 120 150
sample mean 62.7 61.8
sample variance 2.50 2.62
Test the hypothesis, at 5% level, the null hypothesis that the corresponding population means are equal against the alternative that they
are not equal.

Answer 1

Here we wanr to test whether there is a difference between the
average heights of adult females born in two different country
A and country B

Let be the average height of adult female in country A and be the average height of adult female in country B.

The hypothesis is given as

i.e there is no significant difference between the
average heights of adult females born in two different country
A and country B

vs the alternative hypothesis is given as

i.e there is significant difference between the
average heights of adult females born in two different country
A and country B

For random sample from country A

The sample size is

n1 = 120  
sample mean

= 62.7  
sample variance

s₁²=2.50  

For random sample from country B

sample size is

n2 =   150
sample mean

=  61.8
sample variance

s₂²=2.62

Obtaining the pooled variance

The pooled variance will be

= 2.585821

Therefore

s = 1.608049

The test statistic is given as

= 4.569804

Now obtaining the p-value with df = n1 n2 -2

= 268 and t = 4.5698

Since the hypothesis is tow sided the p-value is given as

At 0.05 level of significance

p-value < 0.05

Reject the null hypothesis .

Hence there is sufficient evidence to conclude that there is significant difference between the
average heights of adult females born in two different country
A and country B