Question 1
A busy landscaping supplies company sells wood chips for garden mulch. The mulch is sold by the cubic metre and delivered to households in a small truck. Each truckload is expected to be 4 cubic metres. The company decides to conduct an audit of actual load volumes by measuring a sample of loads for a two-week period. The data file Mulch.xls contains the volume (in cubic metres) from a sample of 368 truckloads of cypress pine wood chips and 330 truckloads of cedar wood chips.
a. For the cypress pine wood chips, construct a 95% confidence interval estimate of the mean volume.
b. For the cedar wood chips, construct a 95% confidence interval estimate of the mean volume.
c. The company is interested to know whether there is a linear relationship between the delivery volumes for the two types of wood chips. Calculate a correlation coefficient for the first 330 pairs of observations and test whether this relationship is significant at the 1% level. Make sure you state the hypotheses that you are testing.
d. Based on the results of (a) and (b), what conclusions can you reach concerning mean volume of the cypress pine wood chips and cedar wood chips?
Question 2
In a random sample of 25 observations from a normal population, we found that the sample mean = 140, and the sample standard deviation = 10. Using a level of significance of 0.05, test the hypothesis that the population mean is 150. You are required to:-
a. State the type of test that you are going to use.
b. State the hypotheses that you are going to test.
c. Calculate the standard error.
d. Calculate the t-statistic.
e. Calculate the p-value.
f. Draw your conclusion.
g. Determine the 95% confidence interval of the population mean and state whether it supports your conclusion given in f) above.
Question 3
The fill amount of soft drink bottles is normally distributed with a mean of 2.0 litres and a standard deviation of 0.05 litres. If you select a random sample of 25 bottles, what is the probability that the sample mean will be...
a. Between 1.99 and 2.0 litres?
b. Below 1.98 litres?
c. Above 2.01 litres?
d. The probability is 99% that the sample mean will contain at least how much soft drink?
Question 4
It is believed that a linear relationship exists between Salary (the dependent variable) and the employees experience measured in years (the independent variable) for Diploma graduates. Using the summary data from a sample of 10 employees:
∑χexperience = 93, ∑χ2= 975, ∑Ysalary = 1014, ∑Y2= 105104, ∑χγ= 9922
a. Provide the regression line equation for this sample. Interpret the coefficient and the intercept.
b. Calculate the standard error of estimate and describe what it tells you about the model fit.
c. Test to determine whether there is enough evidence to infer that a linear relationship exists between experience and salary at the 0.01 significance level. Make sure you state the hypotheses that you are testing.
d. Use your model to predict the expected salary where an employee has 15 years of experience or state why it is not possible to do so.
Question 5
A transport company wishes to predict the price of petrol based on international crude oil prices. They record average monthly petrol prices and crude oil prices over a 12 month period.
|
Month
|
Petrol Price ($/litre)
|
Crude Oil Price ($/barrel)
|
|
January
|
1.25
|
72
|
|
February
|
1.32
|
75
|
|
March
|
1.15
|
69
|
|
April
|
1.35
|
82
|
|
May
|
1.22
|
78
|
|
June
|
1.26
|
80
|
|
July
|
1.43
|
91
|
|
August
|
1.29
|
84
|
|
September
|
1.28
|
82
|
|
October
|
1.17
|
79
|
|
November
|
1.52
|
98
|
|
December
|
1.43
|
91
|
a. Plot a scatter diagram and, assuming a linear relationship, use the least-squares method to calculate the regression equation for this data. You will need to show your calculations for SSX, SSXY, b0 and b1.
b. Interpret the meaning of the Y intercept, b0 and the slope, b1 in this problem.
c. Use the prediction equation developed in (a) to predict the petrol price if crude oil is $75 per barrel.
d. Calculate the coefficient of determination, r2, and interpret its meaning in this problem.
e. Perform a residual analysis on your results and determine whether the sample data meet the linear regression assumption of equal variance (homoscedasticity).
f. At the 0.05 level of significance, is there evidence of a linear relationship between petrol and crude prices? Make sure that you state the hypotheses you are testing.
g. Construct a 95% confidence interval of the population slope.