<h2>
Answer with explanation:</h2>
Let denotes the population mean.
1. Claim : The students in her school district have an IQ higher than the average of 101.5.
As per given , we have
Null hypothesis :
Alternative hypothesis:
∵Alternative hypothesis is right-tailed , this indicates a right-tailed test
Also, Population standard deviation = , we use z-test.
sample size = 30
sample mean =
2. According to the z-table , the critical z-value for the right-tailed test with α = 0.05 is +1.65.
i.e. Critical value = 1.65
3. Test statistic :
Since the calculated z > Critical z value , so we reject the null hypothesis.
We conclude that we have sufficient evidence at α = 0.05 to support the school superintendent claim that the students in her school district have an IQ higher than the average of 101.5.