(b) What is the p-value associated with the sample results? 6. From a population of cans of coffee marked "12 ounces," a sample of 25 cans is selected and the contents of each can are weighed. The sample revealed a mean of 11.8 ounces and a standard deviation of 0.5 ounces. Test to see if the mean of the population is at least 12 ounces. (Assume the population is normally distributed.) Use a 0.05 level of significance. 7. In the past the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 25 employees was selected. The average age in the sample was 45 years with a standard deviation of 5 years. Assume the distribution of the population is normal. Let a = .05. 8. State the null and the alternative hypotheses. 9. Test to determine whether or not the mean age of all employees is signifi- cantly more than 40 years. 10. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. With a 0.05 level of significance, test to see if the machine is in perfect adjustment. Assume the distribution of the population is normal. 11. A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of the population is normal. (a) State the null and alternative hypotheses. (b) Using a critical value, test the hypothesis at the 1% level of sig- nificance. Using a p-value, test the hypothesis at the 1% level of significance. (c) Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8. 12. In a television commercial, the manufacturer of a toothpaste claims that at least 4 out of 5 dentists recommend its product. A consumer-protection group wants to test that claim. Identify the hypotheses. 13. A manufacturer is considering a new production method. The current method produces 94% non-defective (good) parts. The new method will be implemented if it produces more non-defectives than the current method. Identify the hypotheses. 14. new soft drink is being market tested. A sample of 400 individuals par- ticipated in the taste test and 80 indicated they like the taste (a) At a 5% significance level, test to determine if at least 22% of the population will like the new soft drink