It is known from past years that the average IQ of Commack elementary students is at least 110. The principal thinks that this is an overestimate, and that the average IQ of students here is less than 110. The principal administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 104 with a standard deviation of 10. Assume a significance level of 0.05 and conduct a hypothesis test.

Question

Mathematics

Savannah Mckenzie

13 February, 00:49

It is known from past years that the average IQ of Commack elementary students is at least 110. The principal thinks that this is an overestimate, and that the average IQ of students here is less than 110. The principal administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 104 with a standard deviation of 10. Assume a significance level of 0.05 and conduct a hypothesis test.

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Alyssa · Answer 1

The average IQ of Commack elementary students is less than 10

Step-by-step explanation:

Null hypothesis: The average IQ of Commack elementary students is 10

Alternate hypothesis: The average IQ of Commack elementary students is less than 10

Test statistic (z) = (sample mean - population mean) : sd/√n

sample mean = 104, population mean = 110, sd = 10, n = 20

z = (104 - 110) : 10/√20 = - 6 : 2.24 = - 2.68

The test is a one tailed test. The critical value using a 0.05 significance level is 1.645

Conclusion on the null hypothesis: The test statistic (-2.68) is less than the critical value (1.645), reject the null hypothesis

Therefore, the average IQ of Commack elementary students is less than 10.

This result does not support the original claim from past years that the average IQ of Commack elementary students is at least 10.