The probability that machine A will be performing a useful function in five years time is 0.25, while the probability that machine B will still be operating usefully at the end of the same period is 0.33 . Find the probability that at least one of the machines will be operating.

0.4975

0.4940

0.3828

0.2594

0.5767

If the probabilities of Korina, Mary and Chloe being chosen as CEO of Unilever are 0.28, 0.32 and 0.4, respectively,

what is the probability that either Mary or Chloe will become CEO? (Please enter your answer as a value between 0 and 1 to 2 decimal places eg.*.**)

Two companies M and H are in danger of failing, analysts reckon that, in the next year, Pr(M fails) = 0.7, Pr(H fails) = 0.6 and Pr(M and H both fail) = 0.5. What is the probability that both companies survive the next year?

0.24

0.42

0.20

0.10

0.30

A quarter of the customers entering a certain store are less than 25 years old. One percent of the customers less than 25 years old make a major purchase (over £50), and 5% of the customers that are 25 or older make a major purchase. What is the probability that if a major purchase was made, it was by a person of 25 or older?

0.8174

0.7782

0.6346

0.9895

0.9375

How will the area of the rejection region for a two-tailed test compare to area of the rejection of the corresponding one-tailed test with the same significance level?

The area will be larger

The area will be smaller

The area will be the same

A company claims that a new commission policy has resulted in average weekly earning of £380. A random sample of thirty workers is selected and finds that their average weekly earning is £375 and a standard deviation of £30. If the company claim that the average earning is £380, test the company claim at 5% significance level.

Reject Ho

Do not reject Ho

The weights of students in a particular school are normally distributed. A random sample of twenty-five students was chosen. The sample mean is 50 kg and standard deviation of 10 kg. Find a 95% confidence interval for the population mean of the student weight in the school.

(45.56 , 52.44)

(42.5 , 52.5)

(46.08 , 53.92)

(42.36 , 54.64)

A random sample of six cars from a particular model has the following fuel consumption figure, in miles per gallon:

18 16 20 21 19 17

Find a 95% confidence interval for the population mean. Assuming that the population is normal. (Hint: use t-distribution for small sample size).

(14.56, 19.44)

(16.32, 21.68)

(15.32, 20.68)

(16.54, 20.46)

Why might a researcher choose to use a multiple regression specification?

To maximize the likelihood function

Due to stationarity

To avoid the errors-in-variables problem

To include more explanatory variables

Please take a look at the following results for a regression of the height of fully grown adult sons on the height of their fathers.

The intercept is significant at the 1% significance level. True or false?

True

False

Please see the below output for a regression of years live on cigarettes smoked per day and income.

Which estimator is insignificant at the 5% significance level?

the intercept

beta_1

beta_2

The door frames used in an industrialised building system are of one standard size.

If the heights of adults are normally distributed, men with a mean of 1.73m and standard deviation of 0.064m and women with a mean of 1.67 and standard deviation of 0.050m; then what proportion of men will have a clearance of at least 13cm with a frame height of 1.83m?

0.4577

0.68

0.577

0.3196

A random sample of six cars from a particular model has the following fuel consumption figure, in miles per gallon:

18 16 20 21 19 17

Find the sample mean.

18.5

19.8

16.9

17.2

The door frames used in an industrialised building system are of one standard size.

If the heights of adults are normally distributed, men with a mean of 1.73m and standard deviation of 0.064m and women with a mean of 1.67 and standard deviation of 0.050m; then if women outnumber men (e.g. in a department store) in the ratio 19:1, for what proportion of people would a frame height of 1.83m be too low?

0.50

0.0036

1.00

0.9964

Suppose you toss a coin three times.

What is the probability you will get three Tails? (Please enter your answer as a number between 0 and 1 to 3 decimal places, eg.:*.***)

Which of the scenarios below does NOT constitute a panel data set?

The annual returns of 5 hedge funds from 2000 till 2012.

A sample of house prices in London in 1980, and a sample of different London house prices in 2012.

The scores in an IQ test of the same group of children, first when they’re 11, and then later when they reach 12, 13 and 14.

The daily return on the FTSE350, from January 2012 until September 2012.

Which of these is a technique that can be used with panel data?

Difference-in-differences estimators

Variable-variates estimators

Different variables

Random cross-sections

The number of calls to a call centre dealing with new loan applicants is thought to be influenced by the number of television advertisements shown on television the previous night. The regression output is shown below.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.25

R Square 0.50

Standard Error 92.10

Observations 200

Coefficients P-value

Intercept 205.00 0.06

Number of Adverts (x) 37.20 0.40

On average the number of advertisements per night is 5.

Within which of the following intervals would you expect the number of calls to belong following a night with 5 advertisements (with a 95% probability)?

From 132 To 501

From 130 To 580

From 207 to 575

From 207 To 407

The number of calls to a call centre dealing with new loan applicants is thought to be influenced by the number of television advertisements shown on television the previous night. The regression output is shown below.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.25

R Square 0.50

Standard Error 92.10

Observations 200

Coefficients P-value

Intercept 205.00 0.06

Number of Adverts (x) 37.20 0.40

What proportion of the variation in calls is explained by the number of advertisements?

0.5

0.92

0.3

0.25

The number of calls to a call centre dealing with new loan applicants is thought to be influenced by the number of television advertisements shown on television the previous night. The regression output is shown below

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.25

R Square 0.50

Standard Error 92.10

Observations 200

Coefficients P-value

Intercept 205.00 0.06

Number of Adverts (x) 37.20 0.40

How many calls would you expect following an evening with three advertisements?

297

205

652

 

… 317