Question 1:
In recent years, fishermen have suffered financial hardship because of shortened fishing seasons, reduced catches and lower market prices. Moreover, fishermen have complained about price fluctuations and have called for a system of minimum prices One suggestion made was that the size of the catch had an immediate impact on prices, and that this relationship should be clarified before potential solutions were discussed. To investigate this issue, a random 12-week period was selected to study the price of fish versus the average daily catch. The data for the 12 weeks were collected and recorded as follows:
Let x = average daily catch ('00 kg) and y = price per kg ($)
Sum of all x values = 6,970 Sum of all y values = 16.45 Sum of all x-squared values = 4,315,894
Sum of all y-squared values = 24.94
Sum of all xy values = 8,972.8
n = 12
Part (a): Determine the sample regression line that shows the price per kilogram as a function of average daily catch.
Part (b): Calculate the standard error of estimate. What does this value tell you about the relationship between the two variables?
Part (c): Do these data provide sufficient evidence at the 5% significance level to allow you to conclude that large catches result in lower prices?
Part (d): Calculate the coefficient of determination. What does this value tell you about the relationship between the two variables?
Question 2:
Part (a):
The quarterly earnings (in millions of dollars) of a large textile manufacturing company have been recorded for the years 2010-2013. These data are shown in the following table.
Quarter 2010 2011 2012 2013
1 52 57 60 66
2 67 75 77 82
3 85 90 94 98
4 54 61 63 67
Using a four-quarter centred moving average, measure the quarterly variation by calculating the seasonal (quarterly) indexes. Use these to obtain the seasonally adjusted earnings for each of the 16 quarters.
Part (b):
The following trend line and seasonal indexes were calculated from six years of quarterly observations:
Trend line: y^(t) = 2000 + 80t - 2(02) Seasonal indexes:
Quarter Seasonal Index
1 0.6
2 0.9
3 1.1
4 1.4
Forecast the four quarterly values for next year.
Question 3:
The proportion of a companys earnings paid out to its shareholders in the form of dividends is called the company's dividend payout ratio. A frequency distribution of dividend payout ratios (expressed as percentages) for a sample of 125 companies is shown in the following table. Ten of these companies paid no dividend.
Dividend payout ratio (%) Frequency
0 up to 10 13
10 up to 20 7
20 up to 30 10
30 up to 40 23
40 up to 50 28
50 up to 60 21
60 up to 70 14
70 up to 80 5
80 up to 90 3
90 up to 100 1
Part (a):
Using a significance level of 10%, test the hypothesis that dividend payout ratios are normally distributed. (HINT: Combine the three highest classes, since the expected frequencies of the two highest classes are small).
Part (b):
Repeat part (a), considering only companies that paid a dividend. (HINT: Combine the two lowest and three highest classes, since the expected frequencies are small).
Question 4:
An industrial relations expert on academic and non-academic staff has been studying the relationship between gender reporting structures in the workplace and the level of employees' job satisfaction. The results of a recent survey in an institution are shown in the following table.
Level of job satisfaction F/F F/M M/M M/F
Satisfied 20 25 50 75
Neutral 40 50 50 40
Dissatisfied 30 45 10 15
F/F = female supervisor/female employee.
F/M = female supervisor/male employee.
M/M = male supervisor/male employee.
M/F = male supervisor/female employee.
Using the data in the table above, and assuming a significance level of 10%, conduct a test to determine whether the level of job satisfaction depends on the supervisor-employee gender relationship.
Question 5:
Part (a):
An automotive expert claims that the large number of self-serve petrol stations has resulted in poor car maintenance, and that the average lyre pressure is at least 28 kilopascals below its manufacturers specification. As a quick test, 10 tyres are examined, and the number of kilopascals by which each tyre is below specification is recorded The resulting data (in kilopascals) are as follows:
48 62 14 0 34 41 21 34 55 62
Is there sufficient evidence, at a significance level of 5%, to support the expert's claim? State any assumptions that need to be made.
Part (b):
In the 2000 federal election, a candidate received 58% of the ballots cast. Four months later, a survey of 700 people revealed that 54% now supported the candidate. Is this sufficient evidence, at a significance level of 5%, to allow us to conclude that the candidate's popularity has decreased? State any assumptions that need to be made.