Question

Ten participants were recruited for a study on the effect of target size on a psychomotor task. The researcher predicted that larger targets would result in faster psychomotor response. Five participants were randomly assigned to group 1 (large target size) and the other five were randomly assigned to group 2 (small target size). Data are below. Group 1: 9, 6,8,8,9 Group 2: 6,7,7,9,8 What is the obtained value of the most appropriate statistic? What is the critical value for this statistic? Use an alpha of .05 and determine from the wording of the research question (looking at â??faster psychomotor responseâ??) whether this is a directional or a nondirectional test.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁> u₂
Alternative hypothesis: u₁ < u₂

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 1.5951
DF = 10

t = [ (x₁ - x₂) - d ] / SE

t = 0.209

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is thesize of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 0.209

Therefore, the P-value in this analysis is 0.419.

Interpret results. Since the P-value (0.419) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that larger targets would result in faster psychomotor response.

This is directional test.