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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¯ÂÂ¡/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¯ÂÂ­ = 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¯ÂÂ­ = 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¯ÂÂ­ = 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¯ÂÂ­ = 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¯ÂÂ¡/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¯ÂÂ­ = 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¯ÂÂ­ Ã¢â€°Â¥ 185 against the alternative
hypothesis Ã¯ÂÂ­ < 185 at Ã¯ÂÂ¡ = 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¯ÂÂ­ Ã¢â€°Â¥ 185 against the alternative hypothesis Ã¯ÂÂ­ < 185 at Ã¯ÂÂ¡ = 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. Purchase answer to see full attachment

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