In pennsylvania the average iq score is 101.5. the variable is normally distributed, and the population standard deviation is 15. a school superintendent claims that the students in her school district have an iq higher than the average of 101.5. she selects a random sample of 30 students and finds the mean of the test scores is 106.4. test the claim at = 0.05.

We conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

We use one-tailed z test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,  

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

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step-by-step explanation: