Problem: The mean score on the SAT Math Reasoning exam is 518. A test preparation company claims that the mean scores of students who take 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 should not be rejected. State

the conclusion of the company.

Q.3. Suppose, in fact, the mean score of students taking the preparatory course is 522.

Was a Type I or Type II error committed? If we tested this hypothesis at the \(\alpha \) = 0.01 level, what is the probability of committing a Type I error?

Q.4. If we wanted to decrease the probability of making a Type II error, would we need to increase or decrease the level of significance?

To test Ho: \(\mu \) = 40 versus H ₁ : \(\mu \) >40, a random sample of size n = 25 is obtained from a population that is known to be normally distributed with \(\sigma \) = 6.

Q.5. If the sample mean is determined to be \(\bar{X}\) = 42.3, compute the test statistic.

Q.6. If the researcher decides to test this hypothesis at the \(\alpha \) = 0.1 level of significance, determine the critical value.

To test Ho: \(\mu \) = 40 versus H ₁ : \(\mu \) > 40, a simple random sample of size n = 25 is obtained from a population that is known to be normally distributed.

Q.7. If \(\bar{X}\) = 42.3 and s = 4.3, compute the test statistic.

Q.8. If the researcher decides to test this hypothesis at the \(\alpha \) = 0.01 level of significance, determine the critical value.

Q.9. Will the researcher reject the null hypothesis? Why? Let x be the sample proportion.

Ho: p = 0.6 versus H ₁ : p < 0.6, n = 250; x =124; \(\alpha \) = 0.01

Q.10a. Test the hypothesis using the classical approach.

Q.10b. Test the hypothesis using the P-value approach.

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