Question

question 5
developmental psychology researchers have shown a genetic influence of shyness in infants where infants who were adopted were more likely to be rated as shy at 2 years of age if their biological mothers rated themselves as also being shy (daniels & plomin, 1985). a researcher wanted to find out if this finding extended to shyness in identical twins. the researcher recruited a sample of 35 pairs of infants who were identical twins. the researcher asked the infants primary caregiver to rate each infants level of shyness and compared the shyness level between each identical twin to see if there was a mean difference in shyness between the pairs of identical twins.
daniels, d., & plomin, r. (1985). origins of individual differences in infant shyness. developmental psychology, 21, 118 - 121.
if $mu_1$ and $mu_2$ represent the shyness rating of the first - born twin and second - born twin, respectively, and let $mu_d$ be the mean of the differences in the shyness rating (shyness rating of first born - shyness rating of second born) of all identical twins.
which of the following are the appropriate null and alternative hypotheses?
a.
$h_0:mu_d = 0$
$h_a:mu_d>0$
b.
$h_0:mu_d = 0$
$h_a:mu_d
eq0$
c.
$h_0:mu_d
eq0$
$h_a:mu_d = 0$
d.
$h_0:mu_1-mu_2 = 0$
$h_a:mu_1-mu_2
eq0$

Explanation:

The null hypothesis ($H_0$) typically assumes no effect or no difference. Here, the researcher wants to test if there is a mean difference in shyness between identical - twin pairs. So, the null hypothesis should be that the mean difference $\mu_d$ (shyness rating of first - born - shyness rating of second - born) is zero. The alternative hypothesis ($H_a$) is the opposite of the null hypothesis, which is that the mean difference $\mu_d$ is not zero.

Answer:

B. $H_0:\mu_d = 0$
$H_a:\mu_d
eq0$