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Question 1

An insurance company has 10000 automobile policyholders. If the expected yearly claim per

policyholder is $260 with a standard deviation of $800, what is the expected total yearly

claim of all 10000 policyholders?

2600000

8000000

260

26000

Question 2

An insurance company has 10000 automobile policyholders. If the expected yearly claim per

policyholder is $260 with a standard deviation of $800, what is the standard deviation of total

yearly claim of all 10000 policyholders?

8000

800

80000

260

Question 3

An insurance company has 10000 automobile policyholders. If the expected yearly claim per

policyholder is $260 with a standard deviation of $800, calculate the probability that the total

yearly claim exceeds $2.8 million (= 2.8 x 106).

0.006

0.009

0.002

0.013

Question 4

The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm 2. If a

sample of 50 elderly women is taken, what is the probability that their mean height will be within 1 cm of the

mean height of the population of elderly women in the city?

0.48

0.54

0.91

0.76

Question 5

The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm 2. If a

sample of 60 elderly women is taken, what is the probability that their mean height will be less than 158

cm?

0.016

0.023

0.009

0.005

Question 6

Studies have shown that “Melanoma”, a form of skin cancer, kills 15% of Americans who suffer from the

disease each year.

Consider a sample of 10000 melanoma petients. What is the expected value of y, the number of the

10000 melanoma patients who die of this affliction this year?

1000

1500

2500

1200

Question 7

Studies have shown that “Melanoma”, a form of skin cancer, kills 15% of Americans who suffer from the

disease each year.

Consider a sample of 10000 melanoma petients. What is the variance of y, the number of the 10000

melanoma patients who die of this affliction this year?

35.7

1500

1275

89.5

Question 8

Studies have shown that “Melanoma”, a form of skin cancer, kills 15% of Americans who suffer from the

disease each year.

Consider a sample of 10000 melanoma patients. What is the probability that y will exceed 1600 patients

per year?

0.0025

0.094

0.062

0.0085

Question 9

The random variable Y has a Poisson distribution with mean 50. Compute the probability P(Y > 60).

0.09

0.07

0.05

0.03

Question 10

Which of the following statements is TRUE?

The binomial distribution with parameters n and p may be usefully approximated by a normal distribution

with the same mean and variance, N(np, npq), when both np and nq are at most 5.

The binomial distribution with parameters n and p may be usefully approximated by a normal distribution

with the same mean and variance, N(npq, np2), when both np and nq are at least 5. note that q = 1 – p.

The Poisson distribution with parameter Ã‚Âµ may be usefully approximated by a normal distribution with the

same mean and variance, N(Ã‚Âµ, Ã‚Âµ), when Ã‚Âµ is at most 60.

The Poisson distribution with parameter Ã‚Âµ may be usefully approximated by a normal distribution with the

same mean and variance, N(Ã‚Âµ, Ã‚Âµ), when Ã‚Âµ is at least 30.

Question 11

It is important to model machine downtime correctly in simulation studies.

Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an

exponential distribution mean = 60.

Of interest is the mean repair time of a sample of 100 machine breakdowns.

What is the probability that the mean repair time is no longer than 30 minutes?

0.5

0.2

0

0.6

Question 12

It is important to model machine downtime correctly in simulation studies.

Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an

exponential distribution mean = 60.

Of interest is the mean repair time of a sample of 100 machine breakdowns.

What is the variance of the mean repair time?

6000

36

6

60

Question 13

Suppose the average cost of a gallon of unleaded fuel at gas stations is $1.897. Assume that the standard

deviation of such costs is $0.15.

Suppose a random sample of n = 100 gas stations is selected from the population and the cost per gallon

of unleaded fuel is determined for each.

Consider the “sample mean cost per gallon”. What is the approximate probability that the sample has a

mean fuel cost between $1.90 and $1.92?

0.36

0.72

0.18

0.66

Question 14

When we construct the 99% confidence intervals for the population mean (* denoting a confidence

level of 99%), what is the value of ZÃ¯ÂÂ¡/2 used in the computation?

2.575

2.011

1.96

1.645

Question 15

A study was conducted to estimate the mean annual expenditure of SUSS students on textbooks.

Assuming that the expenditure is normally distributed with a population standard deviation $250.

Suppose a random sample of 50 students is drawn and the sample mean is calculated to be $1000.

What is the 95% confidence interval of the population mean?

910.8 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 1055.2

930.7 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 1069.3

845.2 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 1024.3

975.6 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 1077.3

Question 16

Assume that the time patients spend waiting to see the doctor in the polyclinic is normally

distributed. A random sample of 5 observations give the following sample statistics — sample mean

= 30 minutes and sample variance = 86. Suppose the population variance is unknown, what is the

90% confidence interval of the population mean?

19.93 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 35.66

18.40 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 32.97

21.16 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 38.84

19.55 Ã¢â€°Â¤ ÃŽÂ¼ Ã¢â€°Â¤ 37.1

Question 17

The following data from a random sample represents the average daily energy intake in kJ

for each of eleven healthy women:

5260

5470

5640

6180

6390

6515

6805

7515

7515

8230

8770

Interest centred on comparing these data with an underlying mean daily energy intake of

7725 kJ This was the recommended daily intake. Departures from this mean in either

direction were considered to be of interest. Assuming that the population is normal and the

population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of

significance was conducted. The null hypothesis is H0: Ã¯ÂÂ = 7725.

Which test is appropriate to apply for this one population hypothesis problem?

Z test

t test

F test

The maximum likelihood method

Question 18

The following data from a random sample represents the average daily energy intake in kJ

for each of eleven healthy women:

5260

5470

5640

6180

6390

6515

6805

7515

7515

8230

8770

Interest centred on comparing these data with an underlying mean daily energy intake of

7725 kJ This was the recommended daily intake. Departures from this mean in either

direction were considered to be of interest. Assuming that the population is normal and the

population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of

significance was conducted. The null hypothesis is H0: Ã¯ÂÂ = 7725.

What is the value of observed test statistics?

-2.36

-1.76

-2.82

-1.45

Question 19

The following data from a random sample represents the average daily energy intake in kJ

for each of eleven healthy women:

5260

5470

5640

6180

6390

6515

6805

7515

7515

8230

8770

Interest centred on comparing these data with an underlying mean daily energy intake of

7725 kJ This was the recommended daily intake. Departures from this mean in either

direction were considered to be of interest. Assuming that the population is normal and the

population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of

significance was conducted. The null hypothesis is H0: Ã¯ÂÂ = 7725.

What is the degree of freedom df in this problem?

9

8

10

11

Question 20

The following data from a random sample represents the average daily energy intake in kJ

for each of eleven healthy women:

5260

5470

5640

6180

6390

6515

6805

7515

7515

8230

8770

Interest centred on comparing these data with an underlying mean daily energy intake of

7725 kJ This was the recommended daily intake. Departures from this mean in either

direction were considered to be of interest. Assuming that the population is normal and the

population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of

significance was conducted. The null hypothesis is H0: Ã¯ÂÂ = 7725.

In order to make a decision as to whether to accept or reject the null hypothesis, we need to compare

the observed test statistic with the critical value. What is this critical value |tÃ¯ÂÂ¡/2| ?

1.645

1.96

2.143

2.228

Question 21

The following data from a random sample represents the average daily energy intake in kJ

for each of eleven healthy women:

5260

5470

5640

6180

6390

6515

6805

7515

7515

8230

8770

Interest centred on comparing these data with an underlying mean daily energy intake of

7725 kJ This was the recommended daily intake. Departures from this mean in either

direction were considered to be of interest. Assuming that the population is normal and the

population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of

significance was conducted. The null hypothesis is H0: Ã¯ÂÂ = 7725.

What conclusions can be drawn, at the 5% level of significance?

The underlying mean daily energy intake is not equal to 7725 kJ

The underlying mean daily energy intake is equal to 7725 kJ.

The underlying mean daily energy intake is less than 7725 kJ

The underlying mean daily energy intake is greater than 7725 kJ

Question 22

The specifications for a certain kind of ribbon call for a mean breaking strength of 185 pounds.

Suppose five pieces are randomly selected from different rolls. The breaking strengths of these

ribbons are 171.6, 191.8, 178.3, 184.9 and 189.1 pounds. You are required to perform an

appropriate hypothesis test by formulating the null hypothesis Ã¯ÂÂ Ã¢â€°Â¥ 185 against the alternative

hypothesis Ã¯ÂÂ < 185 at Ã¯ÂÂ¡ = 0.05.
What is the value of the observed test statistic?
-1.22
-0.49
-0.78
-1.47
Question 23
The specifications for a certain kind of ribbon call for a mean breaking strength of 185
pounds. Suppose five pieces are randomly selected from different rolls. The breaking
strengths of these ribbons are 171.6, 191.8, 178.3, 184.9 and 189.1 pounds. You are
required to perform an appropriate hypothesis test by formulating the null hypothesis Ã¯ÂÂ Ã¢â€°Â¥ 185
against the alternative hypothesis Ã¯ÂÂ < 185 at Ã¯ÂÂ¡ = 0.05.
What conclusions can be drawn?
No conclusions can be drawn
The null hypothesis cannot be rejected at 5% level of significance
More tests need to be carried out
The null hypothesis will be rejected at 5% level of significance
Question 24
Which of the following is not a condition required for comparing means across multiple
groups using ANOVA?
The data within each group should be nearly normal.
The variability across the groups should be about equal.
The observations should be independent within and across groups.
The means of each group should be roughly equal.
Question 25
Assuming that the height of male students in a large university is normally distributed with
mean 172.7cm and variance 57.76cm2. 80 samples each with 25 male students are
obtained. In how many samples would you expect the sample mean to be between
169.66cm and 173.46cm? Give you answer to one decimal place.
Question 26
In each of the 5 levels of treatment in an ANOVA experiment, the sum of the seven
observed values (A), and the sum of squares of the seven observed values (B) are
recorded as:
Level 1: A = 645, B = 59847
Level 2: A = 721, B = 74609
Level 3: A = 970, B = 134936
Level 4: A = 1017, B = 148367
Level 5: A = 981, B = 138415
What is the value of the F test statistic? Give you answer to 1 decimal place.
Question 27
A certain machine has been producing washers having a mean thickness of 0.125cm. To
determine whether the machine is in proper working order, a sample of 10 washers is
chosen for which the mean thickness is 0.133cm and the variance is 0.000064cm2. Estimate
the p-value for this hypothesis test to 3 decimal places.
Question 28
We are interested to compare the hourly wage (in S$) of cooks of high-end
restaurants in the Core Central Region (CCR), the Rest of Central Region (RCR),
Private Housing Region (PHR), and HDB Estates Region (HDB) of Singapore. From
each region, information of five cooks were collected. The following were calculated
from the data collected:
(i) Total sum of squares of variation = 745.7
(ii) Mean sum of squares of variation due to treatments = 109.6
Give the test statistic value to 2 decimal places.
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