Question

Researchers studying people’s sense of smell devised a measure of smelling ability. A higher score on this scale means the subject can smell better. A random sample of 36 people (18 male and 18 female) were involved in the study. The average score for the males was 10 with a standard deviation of 3.4 and the average score for the females was 11 with a standard deviation of 2.7. Which of the following is the correct standard error for the test evaluating whether the males and females have differing smelling abilities, on average? Choose the closest answer.

Answer 1

Given : s₁ =3.4, n₁=18,

s₂=2.7, n₂ =18

Formula : Standard error = $\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}$

Solution :

Standard error for the test evaluating whether the males and females have differing smelling abilities, on average=

$\sqrt{\frac{3.4^{2}}{18}+\frac{2.7^{2}}{18}}$

=$\sqrt{0.6422+0.405}$

=$\sqrt{1.0472}$

=1.0233