The mean score on the SAT Math Reasoning exam is 518. A testpreparation company claims that the mean scores of students whotake its course are higher than the mean 518.
Q.1. Determine the null and alternative hypotheses.
Q.2. Suppose sample data indicate that the null hypothesis shouldnot be rejected. State the conclusion of the company.
Q.3. Suppose, in fact, the mean score of students taking thepreparatory course is 522. Was a Type I or Type II error committed?If we tested this hypothesis at the α = 0.01 level, what isthe probability of committing a Type I error?
Q.4. If we wanted to decrease the probability of making a Type IIerror, would we need to increase or decrease the level ofsignificance?
To test H0: μ = 40 versus H1: μ>40, a random sample ofsize n = 25 is obtained from a population that is known to benormally distributed with σ = 6.
Q.5. If the sample mean is determined to be x = 42.3, compute thetest statistic.
Q.6. If the researcher decides to test this hypothesis at theα = 0.1 level of significance, determine the critical value.