Answer to Question #287556 in Statistics and Probability for hamna

Question

Two groups were randomly assigned to spend 15 minutes either in a hot room (defined as 30 degrees Celsius) or a cold room (defined as 0 degrees Celsius). After the 15 minutes elapsed, a mood measure was completed by participants. Scores on the measure of mood ranged from 1-20, with higher scores indicating a better mood. Using an alpha of 0.05, test for a difference between the groups. Group 1 (hot) Group 2 (cold) 13 8 12 8 12 5 9 3 8 3 8 2 a)

Answer 1

Solution:

Independent samples t-test is the appropriate analysis as the two groups of participants are not related in any way.

Null Hypothesis (Ho): There is no difference in mood between people in a hot room and a cold room.

Alternative Hypothesis (H1): There is a difference in mood between people in a hot room and a cold room.

The alternative hypothesis is non-directional, therefore the test is two-tailed.

df = n1 + n2 – 2

df = 6 + 6 – 2 = 10

The critical value of t = 2.228

$\begin{gathered} S^{2}=\frac{\sum\left(\mathrm{X}_{1}-\mathrm{M}_{1}\right)^{2}+\sum\left(\mathrm{X}_{2}-\mathrm{M}_{2}\right)^{2}}{n_{1}+n_{2}-2} \quad S^{2}=\frac{25.34+34.84}{6+6-2} \quad S^{2}=\frac{60.18}{10} \quad S^{2}=6.02 \\ t=\frac{\mathrm{M}_{1}-\mathrm{M}_{2}}{\sqrt{\left(\frac{1}{n_{1}}+\frac{1}{n_{2}}\right)} S^{2}} \quad t=\frac{10.33-4.83}{\sqrt{\left(\frac{1}{6}+\frac{1}{6}\right) 6.02}} \quad t=\frac{5.5}{\sqrt{2.01}} \quad t=\frac{5.5}{1.42} \quad t=3.87 \\ \end{gathered}$

The null hypothesis should be rejected as the t-ratio calculated is greater than critical value t.

$r_{\text {effect size }}=\sqrt{\frac{t^{2}}{t^{2}+d f}} \\\quad r_{\text {effect size }}=\sqrt{\frac{3.87^{2}}{3.87^{2}+10}} \\\quad r_{\text {effect size }}=\sqrt{\frac{14.98}{24.98}} \\\quad r_{\text {effect size }}=\sqrt{.5997} \\\quad r_{\text {effect size }}=.77$

This is a strong effect size, therefore the finding is important.

There is a difference in mood when one is in a hot room versus a cold room. This is an important difference. People are in a better mood when in a hot room (M = 10.33) then when in a cold room (M = 4.83).