Question

Hypothesis: Hispanics have larger families than non-Hispanics. The 2008 General Social Survey asked respondents how many children they have. Hispanic respondents had an average of 1.98 children (standard error=0.12), whereas non-Hispanics averaged 1.93 children (standard error=0.04).

A. State the null hypothesis.

B. Calculate the difference between the means.

C. Calculate the standard error of the difference in means.

D. State whether you would accept the null hypothesis or reject it. Explain your reasoning.

Answer 1

a) $H_{0}: \mu _{H}-\mu _{NH}\leq 0$

$H_{0}: \mu _{H}-\mu _{NH}>0$

b) Difference of means = 1.98-1.93 = 0.05

c) Standard error = $\sqrt{0.12*0.12+0.04*0.04}$

= 0.1265

d) $t=(\frac{1.98-1.93}{0.1265})$

= 0.40

Since , test statistic is so less, so we failed to reject the null hypothesis