IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A charter school wants to know if their students have an average IQ that is higher than the population average. They take a random sample of 25 students and find a mean IQ of 108 with a standard deviation of 21. Use a 5% significance level. Be sure to show all of your work and clearly state your conclusion using complete sentences.

I. State the null and alternative hypotheses.

II. Decide on the significance level, .

III. Compute the value of the test statistic.

IV. Determine ap-value, P.

V. If P reject H₀, otherwise do not reject H₀.

VI. Interpret the result of the hypothesis test