In: Statistics and Probability
When people learn a new task, their performance usually improves when they are tested the next day, but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson, 2000). The following data demonstrates this phenomenon. The participants learned a visual discrimination task on one day, and then were tested on the task the following day. Half of the participants were allowed to have at least 6 hours of sleep and the other half were kept awake all night. Is there a significant difference between the two conditions? Use a two tailed test with a = .05. State hypothesis and conclusion Performance Scores Performace
Scores 6 Hours Sleep No sleep
n = 20 n= = 24
M = 72 M=65
SS=932 SS = 706
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1 = u 2
Alternative hypothesis: u1
u 2
Note that these hypotheses constitute a two-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).
s1 = 7.00376
s2 = 5.5404
SE = sqrt[(s12/n1) +
(s22/n2)]
SE = 1.9317
DF = 42
t = [ (x1 - x2) - d ] / SE
t = 3.624
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 40 degrees of freedom is more extreme than -3.624; that is, less than -3.624 or greater than 3.624.
Thus, the P-value = 0.001
Interpret results. Since the P-value (0.001) is less than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that there is significance difference.