An educational researcher is analyzing the test scores for p

An educational researcher is analyzing the test scores for physics students taught using two different methods - a traditional method, and a web-based self-paced method. Can he conclude, at = .05, that the test scores in the web-based self-paced method are lower? Traditional Web-based Self-paced Sample size 1=60 2=40 Mean test score1= 86 2=83 Population variance1=28 2=32. please show work

Solution

Let mu1 be the mean for traditional method

Let mu2 be the mean for web-based self-paced method

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1>mu2 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(86-83)/sqrt(28/60+32/40)

=2.67

It is a right-tailed test.

Given a=0.05, the critical value is Z(0.05) = 1.645 (from standard normal table)

Since Z=2.67 is larger than 1.645, we reject the null hypothesis.

So we can conclude that the test scores in the web-based self-paced method are lower