Which TWO of the following are necessary if forecasts obtained from a time series analysis are to be reliable?

If Σx = 12, Σy = 42, Σx² = 46, Σy² = 542, Σxy = 157 and n = 4, what is the correlation coefficient?

Which TWO of the following are necessary if forecasts obtained from a time series analysis are to be reliable?

A normal distribution has a mean of 60 and a variance of 25.

What is the probability of a score of 72 or more? (to 4 decimal places)

What is the purpose of seasonally adjusting the values in a time series?

Which of the following are common applications of spreadsheets used by management accountants?

1. Variance analysis
2. Cash flow budgeting and forecasting
3. Preparation of financial accounts

Monthly sales have been found to follow a linear trend of y = 9.82 + 4.372x, where y is the number of items sold and x is the number of the month. Monthly deviations from the trend have been calculated and follow an additive model. In month 24, the seasonal variation is estimated to be plus 8.5.

What is the forecast number of items to be sold in month 24? (to the nearest whole number.)

In January, the unemployment in Ruritania is 567,800. If the seasonal factor using an additive time series model is +90,100, what is the seasonally-adjusted level of unemployment? (to the nearest whole number)

A normal distribution has a mean of 650 and a variance of 100.

What is the upper quartile of this distribution?

Which of the following sets of data have the widest spread?

The regression equation Y = 3 + 2X has been calculated from 6 pairs of values, with X ranging from 1 to 10. The correlation coefficient is 0.8. It is estimated that Y = 43 when X = 20.

Which TWO of the following are true?

A normal distribution has a mean of 75 and a variance of 25.

What is the upper quartile of this distribution?

A company must decide between two projects – Project A and Project B. The profits that might be generated from each project are as follows.

Which project should be chosen and what is the associated expected value of profit?

Singers Co is launching a new sewing machine. With television advertising, sales are estimated to achieve the following levels, with associated probabilities.

What is the expected level of sales?

The following question is taken from the June 2013 exam.

An additive time series has the following trend and seasonal variations:

Trend           Y=4,000 + 6X

where           Y= sales in units

X is the number of quarters, with the first quarter of 2014 being 1, the second quarter of 2014 being 2 etc.

Seasonal variation

What is the forecast sales volume for the fourth quarter of 2015?

Under which of the following circumstances would a multiplicative model be preferred to an additive model in time series analysis?

The following information is available for the price of materials used at P Co.

What is Fisher's ideal index?

A normal distribution is to be split into four equal areas, two to the right of Z = 0 and two to the left of Z = 0 (Z = 0 at the mean).

Using normal distribution tables, the |Z| value that splits the area in this way is closest to which of the following?

Using data from twelve European countries, it has been calculated that the correlation between the level of car ownership and the number of road deaths is 0.73.

Which TWO of the statements shown follow from this?

A normal distribution has a mean of 55 and a variance of 14.44.

The probability of a score of 59 or more is approximately which of the following?

Which TWO of the following statements are true?

Which of the following is a feasible value for the correlation coefficient?

A car travels 20 miles at 30 mph, then 10 miles at 60 mph.

What is the mean speed for the whole journey of 30 miles?

The following data represents a time series:

X        36
Y        41      34      38      42

A series of three point moving averages produced from this data has given the first two values as 38 and 39.

What are the values of (X, Y) in the original time series?

The following four data pairs have been obtained: (1, 5), (2, 6), (4, 9), (5, 11). Without carrying out any calculations, which of the following correlation coefficients best describes the relationship between x   and y?

A large publishing company awards a 14% salary increase to every employee.

Which of the following statements about the distribution of the company's salaries is/are correct?

1. The standard deviation will remain unaltered
2. The standard deviation will increase by 14%
3. The coefficient of variation will remain unaltered

Using an additive time series model, the quarterly trend (Y) is given by Y = 65 + 7t, where t is the quarter (starting with t = 1 in the first quarter of 20X5). If the seasonal component in the fourth quarter is –30, what is the forecast for the actual value for the fourth quarter of 20X6, to the nearest whole number?

A normal distribution has a mean of 150 and a variance of 6,944.

What percentage of the population is less than 210? (to two decimal places.)

What is the median of the scores 34, 23, 78, 12, 56, 43, 28, 9, 24 and 87?

Six years ago material M cost $10 per kg and the price index most appropriate to the cost of material M was 130. The same index now stands at 510.

What is the best estimate of the current cost of material M per kg?

Quality control of four independent production processes reveals the length of certain parts (in mm) to be as follows.

Which process has the largest relative variation, as measured by the coefficient of variation?

The coefficient of variation is used to measure which of the following?

A company's management accountant is analysing the reject rates achieved by 100 factory operatives working in identical conditions. Reject rates, Y%, are found to be related to months of experience, X, by this regression equation: Y = 20 – 0.25X. (The correlation coefficient was r = –0.9.)

Using the equation, what is the predicted reject rate for an operative with 12 months' experience?

A spreadsheet is unlikely to be used for which of the following tasks?

The following spreadsheet shows part of a time series analysis of a company’s sales.

What is the four quarter centred moving average of sales units for quarter 4, 2014?

A company uses regression analysis to establish a total cost equation for budgeting purposes.

Data for the past four months is as follows:

The gradient of the regression line is 17.14.

What is the value of a?

A company is bidding for three contracts which are awarded independently of each other. The board estimates its chances of winning Contract A as 50%, of winning Contract B as 1 in 5 and of winning Contract C as 1 in 3. The profits from A, B and C are estimated to be $500,000, $800,000 and $900,000 respectively.

The expected value to the company of the profits from all three contracts will be closest to which of the following?

A normal distribution is to be split into eight equal areas, four to the right of Z = 0 and four to the left of Z = 0 (Z = 0 at the mean).

Using normal distribution tables, the |Z| value that splits the area in this way is closest to which of the following?

A factory employs staff in four departments for which the average (mean) wage per employee per week is as follows.

What is the average (mean) wage per employee per week in this factory?

The weights of component X are normally distributed. The mean weight is 5,200kg and the standard deviation is 430kg.

What is the probability of a component X weighing more than 6,000kg?

Regression analysis is being used to fine the line of best fit (y = a + bx) from eleven pairs of data. The calculations have produced the following information:

Σx = 440, Σy = 330, Σx² = 17,986, Σy² = 10,366 and Σxy = 13,467

What is the value of 'a' in the equation for the line of best fit? (to 2 decimal places)

The trend for monthly sales ($Y) is related to the month (t) by the equation Y = 1,500 – 3t where t = 1 in the first month of 20X8.

What are the forecast sales (to the nearest dollar) for the first month of 20X9 if the seasonal component for that month is 0.92 using a multiplicative model?

A company's annual profits have a trend line given by Y = 20t – 10, where Y is the trend in $'000 and t is the year with t = 0 in 20X0.

What are the forecast profits for the year 20X9 using an additive model if the cyclical component for that year is –30?

Four years ago material X cost $5 per kg and the price index most appropriate to the cost of material X stood at 150.

The same index now stands at 430.

What is the best estimate of the current cost of material X per kg?

A normal distribution has a mean of 150, and a standard deviation of 20.

80% of the distribution is below which of the following (approximately)?

Unemployment numbers actually recorded in a town for the second quarter of the year 2000 were 4,700. The underlying trend at this point was 4,300 people and the seasonal factor is 0.92. Using the multiplicative model for seasonal adjustment, what is the seasonally-adjusted figure (in whole numbers) for the quarter?

A group of shoppers were interviewed and asked how many loaves of bread they would need to buy from the bakers over a one-week period. The results are as follows.

What is the mode of the number of loaves needed per shopper in a one-week period?

The following statements relate to Paasche and Laspeyre indices.

1. Constructing a Paasche index is generally more costly than a Laspeyre index
2. With a Laspeyre index, comparisons can only be drawn directly between the current year and the base year

Which statements are True?

A regression equation Y = a + bX is used to forecast the value of Y for a given value of X.

Which TWO of the following increase the reliability of the forecast?

The following data relates to a company's overhead cost.

Using the high low technique, what is the variable cost per unit (to the nearest $0.01) expressed in current year prices?

Which of the following explains the essence of quota sampling?

In calculating the regression equation linking two variables, the standard formulae for the regression coefficients are given in terms of X and Y.

Which of the following is True?

A large bag of cement cost $0.80 in 20X3. The price indices are as follows.

How much does a bag of cement cost in 20X6 (to 2 dp)?

The following information relates to a company’s semi-variable production overheads.

What is the variable overhead cost per unit, expressed in 2013 prices?

The following scores are observed for the times taken to complete a task, in minutes.

12, 34, 14, 15, 21, 24, 9, 17, 11, 8

What is the median score? (two decimals 00.00)

Over an 18-month period, sales have been found to have an underlying linear trend of y = 7.112 + 3.949x, where y is the number of items sold and x represents the month. Monthly deviations from trend have been calculated and month 19 is expected to be 1.12 times the trend value.

What is the forecast number of items to be sold in month 19?

Production of aluminium tubes is normally distributed with a mean length of 50 cm and a standard deviation of 5 cm.

The percentage of tubes at least 57 cm long is closest to which of the following?

A company sells and manufactures product SX. The selling price of the product is $10 per unit and estimates of demand and variable costs of sales are as follows.

The unit variable costs do not depend on the volume of sales.
Fixed costs will be $30,000.

What is the EV of unit variable costs?

$______  (to 2 decimal places)

A company sells and manufactures product SX. The selling price of the product is $10 per unit and estimates of demand and variable costs of sales are as follows.

The unit variable costs do not depend on the volume of sales.
Fixed costs will be $30,000.

What is the EV of demand?

______ units

The arithmetic mean of the following ten invoice values is $20:

What does $X equal?

A company sells and manufactures product SX. The selling price of the product is $10 per unit and estimates of demand and variable costs of sales are as follows.

The unit variable costs do not depend on the volume of sales.
Fixed costs will be $30,000.

What is the EV of profit?

$______

Based on the last 15 periods the underlying trend of sales is y = 345.12 – 1.35x. If the 16th period has a seasonal factor of –23.62, assuming an additive forecasting model, what is the forecast for that period, in whole units?