Description

Guidelines:

•       you can use Excel, calculators, etc. to verify your work, 

•       but you MUST show ALL your full solutions work on the test paper (no excel or other electronic output will be accepted unless otherwise indicated on a specific question)

Instructions:

Complete the test questions showing all your full solution work and following the guidelines above

1. It has been reported that 62% of college graduates did volunteer work in a recent year. If a sample of 10 college graduates, calculate the following:

a.   The expected number of college graduates who volunteered.  

b.   The expected spread of the number of college graduates who volunteered. 

c.   The shape of the distribution. Ensure you explain your answer.  

d.   The probability that at least 8 college graduates volunteered. 

e.   The probability that at most 2 college graduates volunteered. 

 2. In the refectory of a college both tea and coffee are sold. During the “nonteaching” parts of the day the number of cups of coffee and tea sold per fiveminute interval may be considered to be independent Poisson distributions with means 2.7 and 1.5 respectively. Calculate the probabilities that, in a given five-minute interval,

a.   exactly one cup of coffee and one cup of tea are sold,

b.   exactly two drinks are sold,

c.            more than five drinks are sold.

3. It has been estimated that 17% of mutual fund shareholders are retired persons.  What is the probability that at least 20% of a simple random sample of 400 shareholders is retired?

4. A landscaping firm produces bags of mulch.  Each bag is labeled as 2.5 kilograms.  The mean and standard deviation of the bag filling equipment is set to 2.6 kilograms and 0.08 kilograms. 

a. If the bags are sold in loads of 5 bags, what is the probability that the mean weight of each load is underweight?

5. A tire manufacturer says the tread life of its snow tires can be described by a normal model – mean of 32,000 miles and standard deviation of 2500 miles.

a.   Is it reasonable to hope that the tires will last 39,000 miles? 

b.   What fraction of tires can be expected to last between 28,000 and 33,000 miles? 

c.   Calculate the IQR of the tread life.

6. In the Tax Help Company, 10 employees tax form preparation times are recorded. The sample results yield an average of 39.42 minutes.  It is known that ? = 13.75 ???????.

a.   Calculate the 90% confidence interval for the mean tax form preparation time. 

b.   If the margin of error increases to 9.5 what sample size is needed

7. A study by the Society of Human Resource Management found 23% of Canadian business executives surveyed believe that an employer has no right to read employees’ e-mail.  Assuming that the survey included a random sample of 1200 executives, construct a 90% confidence interval for the proportion of executives in Canada who believe the employers have no right to read employees’ e-mail.

8. A large cinema company regularly tracks the amount movie goers spend when at their theatres. The company reports that the mean amount spent per person is $22.50 with a spread of $5.25. You are a new manager of one of the company’s local theatres and believe the mean amount spent has decreased. You randomly sample 18 theatre patrons and find their mean amount spent per person is $19.50. At the 5% level of significance is there enough evidence to support your belief?

Ensure you are using both the critical value approach and the p-value approach. Include a full conclusion statement with your work.

9. In 1996 31% of students reported that their mothers had graduated from college.  In 2000, responses from 8368 students found that this figure had grown to 32%.  Is this evidence of a change in education level among mothers?  Use a 5% level of significance.

Ensure you are using both the critical value approach and the p-value approach. Include a full conclusion statement with your work.

b)   Determine the linear regression equation.

c)   Calculate the residual for a 10-year-old car.  Show the residual on your graph in part a). Label the observed value, the predicted value and the residual.

d)   Use your equation to estimate the Price of a six-year-old car.

e)   Calculate the correlation coefficient and interpret the meaning of the correlation coefficient in terms of the given variables.

10. You want to examine the relationship between the age and price for used cars sold in the last year by a car dealership company. The following was recorded: