Question

Researchers are interested in whether having an older sibling provides people a model for stable relationships in adolescence. They gather random samples of people with either older siblings or not and measure the number of relationships they have as teenagers. For individuals with no older siblings (N=16), they find an average of 5 relationships (s=1.4) For individuals with older siblings (N=20), they find an average of 3.5 relationships (s=0.8).  Test the null hypothesis that the number of adolescent relationships is equal between those with an older sibling and those without (alpha=0.05).

Answer 1

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 not equal to u2

As the population standard deviation is not given and we are using sample s.d as the best estimate here we will use t distribution to conduct the test

Test statistics t = (x1-x2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

X1 = 5, s1 = 1.4, n1 = 16

X2 = 3.5, s2 = 0.8, n2 = 20

After substitution

t = 3.816

Degrees of freedom is = smaller of n1-1, n2-1

= 15

For 15 dof and 3.816 test statistics

P-value from t distribution is = 0.001687

As the p-value 0.001687 is less than the given significance 0.05

We reject the null hypothesis Ho

So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without