The grade point averages (GPAs) of independent random samples of 17 year-2 stude

Question

The grade point averages (GPAs) of independent random samples of 17 year-2 students and 13 year-3 students at PolyU are shown in Figure 1. The GPA of all year-2 students is normal and the GPA of all year-3 students is normal. At 5% significance level, do the data provide sufficient evidence to conclude that the mean GPA of year-2 students is higher than the mean GPA of year-3 students? Formulate the null and the alternative hypotheses and draw the conclusion (you can use the result in Figure 1).

Explanation / Answer

Hypothesis:

H0 : x1 - x2 = 0

Ha : x1 > x2 = 0

test statistic;

x1 = 2.84 , x2 = 2.22 , s1 = 0.52 , s2 = 1.03 , n1 = 17 , n2 = 13

SE = sqrt [(s12/n1) + (s22/n2)]
SE = sqrt [(0.522/17) + (1.032/13]

= 0.313

t = [ (x1 - x2) - d ] / SE

= [ (2.84 -2.22) - 0 ] / 0.313

= 1.99

Now, we need to find critical value for t = 1.99 and alpha = 0.05

t critical value for right tailed = 1.7011

It provide sufficient evidence to conclude that the mean gpa of 2 year students is higher than mean gpa of 3 year students,

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