Questions - Ka-fu Wong

4. (10 points) A manufacturer of salad dressing uses machines to dispense liquid ingredients intobottles that move along a filling line. The machine that dispenses dressings is working properlywhen 8 ounces are dispensed. The manufacturer is particularly concerned that the bottles do nothave an average of less than 8 ounces. The standard deviation of the process is 0.15 ounce. Asample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence thatthe mean amount dispensed is actually less than 8 ounces. Suppose that the average amountdispensed in a particular sample of 50 bottles is 7.983 ounces.a. (6 points) At the 0.05 level of significance, is there evidence that the mean amountdispensed is less than 8 ounces?b. (4 points) Compute the p-value and interpret its meaning.5. (10 points) The operations manager at a light bulb factory wants to determine whether there isany difference in the average life expectancy of bulbs manufactured on two different types ofmachines. The process standard deviation of Machine I is 110 hours and of Machine II is 125hours. A random sample of 25 light bulbs obtained from Machine I indicates a sample mean of375 hours, and a similar sample of 25 from Machine II indicates a sample mean of 362 hours.a. (6 points) Using the 0.05 level of significance, is there any evidence of a difference in theaverage life of bulbs produced by the two types of machines?b. (4 points) Compute the p-value and interpret its meaning.6. (10 points) The purchasing director for an industrial parts factory is investigating the possibility ofpurchasing a new type of milling machine. She determines that the new machine will be bought ifthere is evidence that the parts produced have a higher average breaking strength than those fromthe old machine. The process standard deviation of the breaking strength for the old machine is10 kilograms and for the new machine is 9 kilograms. A sample of 100 parts taken from the oldmachine indicates a sample mean of 65 kilograms, whereas a similar sample of 100 from the newmachine indicates a sample mean of 72 kilograms.a. (6 points) Using the 0.01 level of significance, is there evidence that the purchasing directorshould buy the new machine?b. (4 points) Compute the p-value and interpret its meaning.7. (14 points) The following is a partial ANOVA table.Source Sum of SquaresDegree ofFreedom Mean Square FTreatment 2Error 0.72947Total 33.918 19a. (5 points) Complete the ANOVA table.b. (1 point) How many treatments are there?c. (1 point) What is the total sample size?d. (2 point) What is the critical value of F, at 0.05 significance level?e. (3 point) Write out the null and alternative hypotheses.f. (2 point) What is your conclusion regarding the null hypothesis at 0.05 significance level?Page 2 of 3

8. (14 points) The following is a partial ANOVA table.Source Sum of SquaresDegree ofFreedom Mean Square FTreatment 3Error 6.094Total 106.7895 19a. (5 points) Complete the ANOVA table.b. (1 point) How many treatments are there?c. (1 point) What is the total sample size?d. (2 point) What is the critical value of F, at 0.05 significance level?e. (3 point) Write out the null and alternative hypotheses.f. (2 point) What is your conclusion regarding the null hypothesis at 0.05 significance level?- END -- END -Page 3 of 3