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Skye Elementary School has 1000 students. The principal of the school thinks that the average IQ of students at is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? State your null and alternative hypotheses, p-value and your conclusion in context of the problem. Use a .05 significance


This question involves a test of hypothesis,  therefore, the first step is to decide the null and the alternative hypothesis to be used. As usual, the null hypothesis will always contain the quality sign. 


H0: mu = 100

Ha: mu < 110>

using an alpha of 0.05,

t = (x_bar - mu)/(s/sqrt(n))

t = (108 - 110)/(10/sqrt(20)) = -0.894

The critical value for this test can be obtained in excel using the t.inv() Function,  =T.INV(0.05,19) = -1.729

The criteria is to reject th null hypothesis if the test test statistic (t - test) which follows a t distribution is less than the critical value (-1.729)

Alternatively, the p -value for this test can be calculated in excel using the = T-DIST() function, =T.DIST(-0.894,19,TRUE) = 0.191, 

And the null hypothesis is rejected in the p value is less than, In this case, the p value is greater than 0.05, therefore, the null hypothesis is not rejected. There is not sufficient evidence to reject the professor's claim. 


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