problem 1:
A busy landscaping supplies company sells wood chips for garden mulch. The mulch is sold through the cubic meter and delivered to households in a small truck. Each truckload is expected to be 4 cubic meters. 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 includes the volume (in cubic meters) from a sample of 368 truckloads of cypress pine wood chips and 330 truckloads of cedar wood chips.
a) For cypress pine wood chips, construct a 95% confidence interval estimate of the mean volume.
b) For 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 among the delivery volumes for the two kinds of wood chips. Compute a correlation coefficient for the first 330 pairs of observations and test whether this relationship is important at the 1% level. Make sure you state the hypotheses which you are testing.
d) Based on the outcomes of (a) and (b), what conclusions can you reach concerning mean volume of the cypress pine wood chips and cedar wood chips?
problem 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. By using a level of significance of 0.05, test the hypothesis that the population mean is 150.You are needed to:-
a) State the kind of test which you are going to use.
b) State the hypotheses which you are going to test.
c) Compute the standard error.
d) Compute the t-statistic.
e) Compute the p-value.
f) Draw your conclusion.
g) Find out the 95% confidence interval of the population mean and state whether it supports your conclusion given in f) above.
problem 3:
The fill amount of soft drink bottles is normally distributed with the mean of 2.0 liters and a standard deviation of 0.05 liters. When you select a random sample of 25 bottles, determine the probability that the sample mean will be:
a) Between 1.99 and 2.0 liters?
b) Below 1.98 liters?
c) Above 2.01 liters?
d) The probability is 99% that the sample mean will include at least how much soft drink?
problem 4:
This 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. By using the summary data from a sample of 10 employees:
Σ X_{experience} = 93, Σ X^{2} = 975, Σ Y_{salary} = 1014, Σ Y^{2} = 105104, Σ X Y = 9922
a) Give the regression line equation for this sample. Interpret the coefficient and the intercept.
b) Compute the standard error of estimate and describe what it tells you about the model fit.
c) Test to find out whether there is adequate evidence to infer that a linear relationship exists between experience and salary at the 0.01 significance level. Make sure you state the hypotheses which 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.
problem 5:
The transport company wishes to expect 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.
a) Plot a scatter diagram and supposing a linear relationship, use the least-squares technique to compute the regression equation for this data. You will require to show your computations for SSX, SSXY, and;
b) Interpret the meaning of the Y intercept and the slope, in this problem.
c) Use the prediction equation developed in (a) to predict the petrol price when crude oil is $75 per barrel.
d) Compute the coefficient of determination, r^{2}, and interpret its meaning in this problem.
e) Perform a residual analysis on your results and find out whether the sample data meet the linear regression assumption of equal variance (homoscedasticity).
f) At 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) Make a 95% confidence interval of the population slope.