Question 1:

An agent for a residential real estate company in a large city would like to be able to

predict the weekly rental cost for apartments based on the size of the apartment as

defined by the number of square metres in area. A sample of 25 apartments was selected

from across the city, and the information gathered recorded in the following table:

(a) What are the dependent and independent variables in this problem? Explain.

(b) Use the least-squares method to find the regression coefficients (show workings). State

the simple linear regression equation.

(c) Interpret the meaning of both regression coefficients in this problem.

(d) Predict the weekly rental cost for an apartment that has an area of 100 square metres.

(e) Would it be appropriate to use the model to predict the weekly rental for an apartment

that has an area of 50 square metres? Explain.

(f) Your friends are considering signing a lease for an apartment in this city. They are

trying to decide between two apartments, one with an area of 100 square metres for a

weekly rent of $294 and the other with an area of 120 square metres for a weekly rent of

$329. What would you recommend to them? Why?

Question 2:

Refer to the tabulated sample data in Question 1 relating to weekly rental cost for

apartments based on the size of the apartment as defined by the number of square metres

in area.

(a) Calculate the coefficient of linear correlation (show workings). What does this value

indicate regarding the relationship between size of apartment and weekly rental cost?

(b) Showing all workings, compute the estimated standard error of regression (slope).

(c) At the 5% level of significance, test for evidence of a linear relationship between the

size of the apartment and the weekly rent.

(d) Compare and comment on the results obtained in parts (a) and (c).

Question 3:

In a certain jurisdiction, savings banks are allowed to sell a form of life insurance to their

customers. The approval process consists of underwriting, which includes a review of the

application, a medical information statement check, possible requests for additional

medical information and medical examinations, and a policy compilation stage where the

policy pages are produced and sent to the bank for delivery. The ability to deliver approved

policies to customers in a timely manner is critical to the profitability of this service to the

bank. During a period of 1 month, a random sample of 27 approved policies was selected

and the total processing time in days was recorded with the following results:

(a) In the past, suppose that the mean processing time averaged 45 days. At the 5% level

of significance, is there evidence that the mean processing time has changed from 45

days?

(b) What assumption about the population distribution must be made in part (a)?

(c) Do you think that the assumption made in part (b) has been seriously violated? Explain.

(HINT: compute the 5-number summary for the data and analyse the results)

Question 4:

The inspection division of a government department is interested in determining whether

the proper amount of soft drink has been placed in 2-litre bottles at the local bottling plant

of a large nationally known soft drink producing company. The bottling plant has informed

the inspection division that the standard deviation of bottle fill for 2-litre bottles is 0.05 litre.

A random sample of 100 2-litre bottles obtained from this bottling plant indicates a sample

mean bottle fill of 1.99 litres.

(a) At the 5% level of significance, use the critical value approach to test for evidence that

the mean amount of soft drink in the bottles is different from 2.0 litres.

(b) Compute the p-value (probability value) and interpret its meaning.

(c) Set up a 95% confidence interval estimate of the population mean amount of soft drink

in the bottles.

(d) Compare the results in parts (a) and (c). What conclusions do you reach from this

comparison?

Question 5:

During the first half of a recent calendar year the share market was quite volatile and many

major share indexes declined. Assume that the returns for funds invested in shares during

this time period are normally distributed with a mean of -10.0% (that is, a loss) and a

standard deviation of 8.0%.

(a) Find the probability that a share fund lost 18% or more.

(b) Find the probability that a share fund gained in value.

(c) Find the probability that a share fund gained at least 10%.

(d) The return for 80% of share funds was greater than what value?

(e) The return for 90% of share funds was less than what value?

(f) 95% of share funds had returns between what two values symmetrically distributed

around the mean? 

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