Assignment Details

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?

Group of answer choices

1. 260
2. 26000
3. 8000000
4. 2600000

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 the total yearly claim of all 10000 policyholders?

Group of answer choices

1. 260
2. 800
3. 80000
4. 8000

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)

Group of answer choices

1. 0.006
2. 0.002
3. 0.009
4. 0.013

Question 4

Given that the mean contents of bags of salt labeled as containing 1 kg is 1003 g and that the standard deviation of their contents is 2 g. Suppose a random sample of 5 bags is taken. What is the expected value of the total contents of a sample of 5 bags?

Group of answer choices

1. 4995
2. 5015
3. 4550
4. 4725

Question 5

Given that the mean contents of bags of salt labeled as containing 1 kg is 1003 g and that the standard deviation of their contents is 2 g. Suppose a random sample of 5 bags is taken. What is the standard deviation of the total contents of a sample of 5 bags?

Group of answer choices

1. 4.472
2. 4.122
3. 4.595
4. 4.982

Question 6

Given that the mean contents of bags of salt labeled as containing 1 kg is 1003 g and that the standard deviation of their contents is 2 g. Suppose a random sample of 5 bags is taken. What is the expected value of the mean contents of a sample of 5 bags?

Group of answer choices

1. 1003
2. None of the above
3. 2006
4. 5015

Question 7

Given that the mean contents of bags of salt labeled as containing 1 kg is 1003 g and that the standard deviation of their contents is 2 g. Suppose a random sample of 5 bags is taken. What is the variance of the mean contents of a sample of 5 bags?

Group of answer choices

1. 0.8
2. 0.6
3. 0.7
4. 0.9

Question 8

Given that the mean contents of bags of salt labeled as containing 1 kg is 1003 g and that the standard deviation of their contents is 2 g. Suppose a random sample of 5 bags is taken. Assuming that the contents of the bags of salts are normally distributed. What is the probability that the mean contents of a sample of 5 bags will be less than 1 kg?

Group of answer choices

1. 0.0009
2. 0.0002
3. 0.0007
4. 0.0004

Question 9

The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm2. 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?

Group of answer choices

1. 0.91
2. 0.54
3. 0.48
4. 0.76

Question 10

The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm2. If a sample of 60 elderly women is taken, what is the probability that their mean height will be less than 158 cm?

Group of answer choices

1. 0.016
2. 0.023
3. 0.005
4. 0.009

Question 11

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 expected value of y, the number of the 10000 melanoma patients who die of this affliction this year?

Group of answer choices

1. 1200
2. 1500
3. 1000
4. 2500

Question 12

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 variance of y, the number of the 10000 melanoma patients who die of this affliction this year?

Group of answer choices

1. 1275
2. 1500
3. 35.7
4. 89.5

Question 13

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?

Group of answer choices

1. 0.094
2. 0.0085
3. 0.062
4. 0.0025

Question 14

The random variable Y has a Poisson distribution with mean 50. Find an approximate value for the probability P(Y > 60).

Group of answer choices

1. 0.05
2. 0.09
3. 0.07
4. 0.03

Question 15

Which of the following statements is TRUE?

Group of answer choices

1. 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.
2. 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.
3. The Poisson distribution with parameter µ may be usefully approximated by a normal distribution with the same mean and variance, N(µ, µ), when µ is at most 60.
4. The Poisson distribution with parameter µ may be usefully approximated by a normal distribution with the same mean and variance, N(µ, µ), when µ is at least 30.

Question 16

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?

Group of answer choices

1. 0.2
2. 0.5
3. 0
4. 0.6

Question 17

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?

Group of answer choices

1. 6
2. 36
3. 60
4. 6000

Question 18

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?

Group of answer choices

1. 0.36
2. 0.18
3. 0.66
4. 0.72

Question 19

When we construct the 99% confidence intervals for the population mean (* denoting a confidence level of 99%), what is the value of Za/2 used in the computation?

Group of answer choices

1. 2.575
2. 1.96
3. 2.011
4. 1.645

Question 20

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 of $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?

Group of answer choices

1. 910.8 ≤ μ ≤ 1055.2
2. 975.6 ≤ μ ≤ 1077.3
3. 930.7 ≤ μ ≤ 1069.3
4. 845.2 ≤ μ ≤ 1024.3

Question 21

Assume that the time patients spend waiting to see the doctor in the polyclinic is normally distributed. A random sample of 5 observations gives 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?

Group of answer choices

1. 19.93 ≤ μ ≤ 35.66
2. 21.16 ≤ μ ≤ 38.84
3. 19.55 ≤ μ ≤ 37.1
4. 18.40 ≤ μ ≤ 32.97

Question 22

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 centered 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: u= 7725.

An appropriate test for this one population hypothesis problem is to use the _______.

Group of answer choices

1. t test
2. The maximum likelihood method
3. F test
4. Z test

Question 23

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 centered 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:= 7725m.

What is the value of observed test statistics?

Group of answer choices

1. -1.45
2. -2.82
3. -2.36
4. -1.76

Question 24

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: u = 7725.

What is the degree of freedom df in this problem?

Group of answer choices

1. 10
2. 9
3. 8
4. 11

Question 25

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 centered 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: u= 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 |t/2|?

Group of answer choices

1. 1.96
2. 2.228
3. 2.143
4. 1.645

Question 26

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 centered 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: u= 7725.

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

Group of answer choices

1. The underlying mean daily energy intake is not equal to 7725 kJ
2. The underlying mean daily energy intake is less than 7725 kJ
3. The underlying mean daily energy intake is greater than 7725 kJ
4. The underlying mean daily energy intake is equal to 7725 kJ.

Question 27

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 u ≥ 185 against the alternative hypothesis u< 185 at a= 0.05.

What is the value of the observed test statistic?

Group of answer choices

1. -1.22
2. -1.47
3. -0.49
4. -0.78

Question 28

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 < 185 at a= 0.05.

What conclusions can be drawn?

Group of answer choices

1. No conclusions can be drawn
2. The null hypothesis will be rejected at 5% level of significance
3. The null hypothesis cannot be rejected at 5% level of significance
4. More tests need to be carried out

Question 29

An industrial plant discharges water into a river. An environmental protection agency has studied the discharged water and found the lead concentration in the water (in micrograms per liter) has a normal distribution with a population standard deviation σ = 0.7 μg/l. The industrial plant claims that the mean value of the lead concentration is 2.0 μg/l. However, the environmental protection agency took 10 water samples and found that the mean is 2.56 μg/l. A hypothesis test is carried out to determine whether the lead concentration population mean is higher than the industrial plant claims. (Use 1% level of significance).

An appropriate test for this one population hypothesis problem is to use the _______.

Group of answer choices

1. Two-sided t test
2. Upper one-sided Z test
3. Upper one-sided t test
4. Two-sided Z test

Question 30

An industrial plant discharges water into a river. An environmental protection agency has studied the discharged water and found the lead concentration in the water (in micrograms per liter) has a normal distribution with a population standard deviation σ = 0.7 μg/l. The industrial plant claims that the mean value of the lead concentration is 2.0 μg/l. However, the environmental protection agency took 10 water samples and found that the mean is 2.56 μg/l. A hypothesis test is carried out to determine whether the lead concentration population mean is higher than the industrial plant claims. (Use 1% level of significance).

The observed test statistic is calculated to be _________

Group of answer choices

1. 3.85
2. 4.26
3. 1.64
4. 2.53

Question 31

An industrial plant discharges water into a river. An environmental protection agency has studied the discharged water and found the lead concentration in the water (in micrograms per liter) has a normal distribution with a population standard deviation σ = 0.7 μg/l. The industrial plant claims that the mean value of the lead concentration is 2.0 μg/l. However, the environmental protection agency took 10 water samples and found that the mean is 2.56 μg/l. A hypothesis test is carried out to determine whether the lead concentration population mean is higher than the industrial plant claims. (Use 1% level of significance).

By comparing the observed test statistic with the critical values, which of the following conclusions is correct?

Group of answer choices

1. No conclusion can be made at this point in time, as more sample data are needed for further analysis.
2. There is not enough evidence to infer that the lead concentration population mean is higher than the industrial plant claims.
3. There is sufficient evidence to infer that the lead concentration population mean is higher than the industrial plant claims.
4. None of the above.

Question 32

The “p-value” is also known as ________:

Group of answer choices

1. Type II error
2. power of the hypothesis test
3. Type I error
4. significant probability

Question 33

Suppose the monthly rents of 3-room HDB flats in a particular constituency are normally distributed with a mean of US$780 and a standard deviation of US$150. Samples of 9 flats are randomly selected. Compute the probability that the mean monthly rent of 3-room HDB flats is more than US$825.

Group of answer choices

1. 0.096
2. 0.297
3. 0.356
4. 0.184

Question 34

Suppose the monthly rents of 3-room HDB flats in a particular constituency are normally distributed with a mean of US$780 and a standard deviation of US$150. Samples of 9 flats are randomly selected. Compute the standard error of the mean.

Group of answer choices

1. (150)(150)
2. (50(50)
3. 50
4. 150

Question 35

Based on a level of significance of 5%, a particular hypothesis test was conducted on the population mean. It was found that the p-value is 0.00028. What conclusion can we draw?

Group of answer choices

1. There is strong evidence to reject the null hypothesis
2. There is moderate evidence to reject the null hypothesis
3. Do not reject the null hypothesis
4. There is little evidence to reject the null hypothesis