Reference no: EM13342749

Question 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 330 mL. The population standard deviation of the amount dispensed is 4 mL. 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.

a) Perform a hypothesis test (using either the p-value approach or critical value approach) to see if there is evidence that the population mean amount is different from 330 mL. (Use a 0.05 level of significance).

b) What would be your answer in (a) if the standard deviation is instead 0.9 mL?

c) What would be your answer in (a) if the sample mean is 328.9 mL and the standard deviation is 3 mL?


Question 2:

The energy consumption of refrigerators sold in a country is checked and appliances are given a star rating to guide consumers who are about to make purchases. The consumption in kWh per annum is also displayed for each model on the government website. Suppose a consumer organisation wants to estimate the actual electricity usage of a model of refrigerator that has an advertised energy usage of 439 kWh per annum. It tests a random sample of 18 fridges and finds a sample mean usage of 445 and a sample standard deviation of 40.

a) Assuming that the energy usage in the population is normally distributed, construct a 95% confidence interval estimate of the population mean energy usage for this model of refrigerator.

b) Do you think that the consumer organisation should accuse the manufacturer of producing fridges that do not meet the advertised energy consumption? Explain.

Question 3:

The head of research and development (R&D) of a large chemical manufacturing company believes that the company's annual profits depend on the amount spent on R&D. The new chief executive officer disagrees and has asked for evidence. The head of R&D therefore wants an equation for predicting annual profits from the amount budgeted for R&D.

The following table presents relevant historical information for the preceding 6 years.

Let X = Amount Spent on R&D, and Y = Annual Profit (both in $ million):

Year  X   Y   XY    X^2
         
2006  2  20  40     4
2007  3  25  75     9
2008  5  34  170   25
2009  4  30  120   16
2010  11 40 440  121
2011  5  31  155    25
        
Totals  30  180  1,000  200
   

a) Use the least-squares method to derive the linear regression equation describing the relationship between R&D expenditure and annual profit.

b) Use the regression equation to predict annual profit in 2012 if the company budgets to spend $8 million for R&D that same year.

c) Would it be meaningful to use the regression equation to predict annual profit if the company decided to double R&D expenditure to $16 million in 2012? Explain reasoning.


Question 4:

The weight of any passenger using a ferry service has a normal distribution with mean 168 pounds and standard deviation 19 pounds. A particular ferry carries 25 passengers. Safety regulations state that for this particular ferry, the total weight of passengers on the boat should not exceed 4,250 pounds more than 5% of the time.

a) Find the probability that the total weight of passengers on the ferry will exceed 4,250 pounds.

b) Find the 95th percentile of the distribution of the total weight of passengers on the ferry.

c) Is the ferry complying with safety regulations? Explain reasoning.