A study was done on proctored and nonproctored tests The res

A study was done on proctored and nonproctored tests. The results are shown in the table Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations arc equal. Complete the parts below. Use a 0.05 significance level, and test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. What are the null and alternative hypotheses? The test statistic, t, is The P-value is State the conclusion for the test.

Solution

Standard error. Compute the standard error (SE) of the sampling distribution.
SE = sqrt( (s1^2/n1) + (s2^2/n2) )
= sqrt( ((10.21)^2/31) + ((20.37)^2/35) )
= 3.901

Test statistic. The test statistic is a t-score (t) defined by the following equation.
t = ( (x1 - x2) - d ) / SE
= (78.62 - 86.67 - 0)/ 3.901
= -2.06 Answer

dF = n1+n2-1 = 31 + 35 -2 = 64
alpha = 0.05

Therefore from t table,

P-value = 0.022 Answer