Hi i need help for these questions? i need with all calculation.

Chapter 9

1) A manufacturer of salad dressings uses machines to dispense liquid ingredients intobottles that move along a filling line. The machine that dispenses dressings is workingproperly when the mean amount dispensed is 330ml. The population standarddeviation 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 isdifferent from 330 ml. Suppose that the mean amount dispensed in a particular sampleof 50 bottles is 329.7 ml.

a) Is there evidence that the population mean amount is different from 330ml? (Use a0.05 level of significance)

b) Calculate the p value and interpret its meaning.

c) What is your answer in (a) if the standard deviation is 0.9 ml?

d) What is your answer in (a) if the sample mean is 328.9 ml and the standarddeviation is 3 ml?

2) *We test 50 American children and find that average level of cholesterol of thesample is 198. We know the population standard deviation is 15. It is known that themean cholesterol level for all Americans is 190.

a) Do we have evidence to suggest that American children have an average highercholesterol level than the national average? (Use a 0.05 level of significance).

b) At the 0.05 level of significance, use the p value approach.c) Interpret the meaning of the p value.

3) A manufacturer of chocolate-coated sweets uses machines to package the sweets asthey move along a filling line. Although the packages are labeled as 250 g, the company 2wants the packages to contain 250.4 g so that virtually none of the packages containsless than 250 g. A sample of 50 packages is selected periodically and the packagingprocess is stopped if there is evidence that the mean amount packaged is different from250.4 g. Suppose that the mean amount dispensed in a particular sample of 50 packagesis 250.35 g with a sample standard deviation of 0.2g. Is there evidence that thepopulation mean amount is different from 250.4 g? (Use a 0.05 level of significance)

4) *50 smokers were questioned about the number of hours they sleep each day. Thesample mean is 7.5 and standard deviation is 0.5. Is there evidence that the smokersneed less sleep than the general public which needs an average of 7.7 hours of sleep(=0.05).

5) For the 2009-10 period, it was reported that Australia wide 79.5% of GP servicesunder Medicare were bulk billed. Suppose that the Government proposes to makechanges to scheduled fees and carries out a survey to see whether generalpractitioners will bulk bill under the new arrangements. The survey shows that 402of 500 will bulk bill.

a) At the 0.01 level of significance, is there evidence that the proportion of medicalpractitioners who bulk bill will change from 79.5% under the new arrangements?

b) Calculate the p value and interpret its meaning.

6) *A recent survey in a town showed that most of people support candidate A in thelocal election. The poll of 500 adults was conducted and 400 of them supportedcandidate A. Perform the hypothesis test at 10% level of significance to find outwhether the fraction of people will support candidate A in the next election will be morethan 75%.