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 α = 0.05

1. state the hypotheses and identify the claim. h0: μ=101.5h1: μ> 101.5this is the claim, and this indicates a right-tailed test
2. find the critical value. for a right-tailed test with α = 0.05, the z-value is +1.65.
3. compute the test statistic.

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.