Chapter 9

Note: Questions with * are covered in the tutorial.

1. *A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when the mean amount dispensed is 330ml. The population standard deviation of the amount dispensed is 4ml. A sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 330 ml. Suppose that the mean amount dispensed in a particular sample of 50 bottles is 329.7 ml,
2. Is there evidence that the population mean amount is different from 330ml? (Use a 0.05 level of significance).
3. Calculate the p value and interpret its meaning.
4. What is your answer in (a) if the standard deviation is 0.9 ml?
5. What is your answer in (a) if the sample mean is 328.9 ml and the standard deviation is 3ml?

1. *We test50American children and find that average level of cholesterol of the sample is 198. We know the population standard deviation is 15. It is known that the mean cholesterol level for all Americans is190.
2. Do we have evidence to suggest that American children have an average higher cholesterol level than the national average? (Use a 0.05 level of significance).
3. At the 0.05 level of significance, use the p value approach.
4. Interpret the meaning of the p value.

1. A manufacturer of chocolate-coated sweets uses machines to package the sweets as they move along a filling line. Although the packages are labeled as 250 g, the company wants the packages to contain 250.4 g so that virtually none of the packages contains less than 250 g. A sample of 50 packages is selected periodically and the packaging process is stopped if there is evidence that the mean amount packaged is different from 250.4 g. Suppose that the mean amount dispensed in a particular sample of 50 packages is 250.35 g with a sample standard deviation of 0.2g. Is there evidence that the population mean amount is different from 250.4 g? (Use a 0.05 level of significance)

1. *50smokers were questioned about the number of hours they sleep each day. The sample mean is7.5and standard deviation is0.5. Is there evidence that the smokers need less sleep than the general public which needs an average of7.7hours of sleep (=0.05)?

1. For 2009-10, in Australia, 79.5% of general practitioner doctor services under Medicare were bulk billed. Suppose that the Government proposes to make changes to scheduled fees and carries out a survey to see whether general practitioners will bulk bill under the new arrangements. The survey shows that 402 of 500 will bulk bill.
2. At the 0.01 level of significance, is there evidence that the proportion of general practitioners who bulk bill will change from 79.5% under the new arrangements?
3. Calculate the p value and interpret its meaning.

1. *A recent survey in a town showed that most of people support candidate A in the local election. The poll of 500 adults was conducted and 400 of them supported candidate A. Perform the hypothesis test at 10% level of significance to find out whether the fraction of people will support candidate A in the next election will be more than 75%.