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MTH220 Jan21 CMA01 Jan 2021

 


CMA01

  • Due 14 Apr at 23:55
  •  
  • Points 100
  •  
  • Questions 28
  •  
  • Available 7 Apr at 23:55 - 14 Apr at 23:55 7 days
  •  
  • Time limit None

Instructions

Deadline for MTH220 / CMA01 submission --- latest by Wednesday, 14 Apr 2021, 2355 hrs.

The CMA will be available from 7 April 2021 , 23:55 hours to 14 April 2021 , 23 55 hours.

Attempt history

AttemptTimeScore
LATESTAttempt 160 minutes100 out of 100
 Correct answers are hidden.
Score for this quiz: 100 out of 100
Submitted 14 Apr at 0:27
This attempt took 60 minutes.
 
Question 1
/ 3 pts
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?
  
  
  
  
 
Question 2
/ 3 pts
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?
  
  
  
  
 
Question 3
/ 3 pts
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)
  
  
  
  
 
Question 4
/ 3 pts
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?
  
  
  
  
 
Question 5
/ 3 pts
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?
  
  
  
  
 
Question 6
/ 3 pts

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?

  
  
  
  
 
Question 7
/ 3 pts

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?

  
  
  
  
 
Question 8
/ 3 pts

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?

  
  
  
  
 
Question 9
/ 3 pts
The random variable Y has a Poisson distribution with mean 50. Compute the probability P(Y > 60).
  
  
  
  
 
Question 10
/ 3 pts
 Which of the following statements is TRUE?
  
  
  
  
 
Question 11
/ 3 pts

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?

  
  
  
  
 
Question 12
/ 3 pts

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?

  
  
  
  
 
Question 13
/ 3 pts

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?

  
  
  
  
 
Question 14
/ 3 pts
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?                                    
  
  
  
  
 
Question 15
/ 3 pts
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?         
  
  
  
  
 
Question 16
/ 3 pts
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?                  
  
  
  
  
 
Question 17
/ 1 pts

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 H0m = 7725.

 

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

 

 

  
  
  
  
 
Question 18
/ 3 pts

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 H0m = 7725.

What is the value of observed test statistics?           

 

 

 

 

 

  
  
  
  
 
Question 19
/ 3 pts

   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 H0m = 7725.

 

 

What is the degree of freedom df in this problem?       

 

 

 

 

  
  
  
  
 
Question 20
/ 3 pts

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 H0m = 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 |ta/2| ?                            

 

 

 

 

  
  
  
  
 
Question 21
/ 3 pts

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 H0m = 7725.

 

 

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

 

 

  
  
  
  
 
Question 22
/ 3 pts

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

What is the value of the observed test statistic?

 

  
  
  
  
 
Question 23
/ 3 pts

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

 

      What conclusions can be drawn?

 

  
  
  
  
 
Question 24
/ 1 pts
Which of the following is not a condition required for comparing means across multiple groups using ANOVA?
  
  
  
  
 
Question 25
/ 8 pts

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
/ 8 pts

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
/ 8 pts

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
/ 8 pts

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.

Quiz score: 100 out of 100

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