Find the P-values while (hypothesis) testing mean. The principal of a school wan

Question

Find the P-values while (hypothesis) testing mean.
The principal of a school wants to test the average IQ of students at her school. She administers an IQ test to 36 randomly selected students. Among the sampled students, the sample average IQ is 108.
a) What is the P-value when testing the hypothesis that the average IQ is at least 110? Assume that population standard deviation is known to be 10.
P-value = (round to 4 decimals)

b) What is the P-value when testing the hypothesis that the average IQ is at most 110? Assume that the sample standard deviation is known to be 10.
P-value = (round to 4 decimals)

c) What is the P-value when testing the hypothesis that the average IQ is not 110? Assume that population standard deviation is known to be 10.
P-value = (round to 4 decimals)

Explanation / Answer

Test statistic = (X bar - mean) / (sd /sqrt (n))

= (108 - 110) / (10 / sqrt(36))

= - 1.2

A)p-value = P(Z > - 1.2) = 1 - P(Z < - 1.2) = 1 - 0.1151 = 0.8849

B) P-value = P(Z< - 1.2) = 0.1151

C) p-value = 2 * P(Z < - 1.2) = 2 * 0.1151 = 0.2302

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