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We have that
The hypothesis test is right-tailed.
The population standard deviation is known and the sample size is large (n≥30) so we use z-test.
Let the significance level be 5% in this test, therefore Z0.05 = 1.64
The critical region is Z > 1.64
Since 4.38 > 1.64 thus the Ztest falls in the rejection region we reject the null hypothesis.
At the 5% significance level the data do provide sufficient evidence to support the claim. We are 95% confident to conclude that the students in the school are above average intelligence.