Question 13 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?
Group of answer choices
260
2600000
26000
8000000
Flag question: Question 2
Question 23 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?
Group of answer choices
800
260
8000
80000
Flag question: Question 3
Question 33 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)
Group of answer choices
0.002
0.009
0.013
0.006
Flag question: Question 4
Question 43 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?
Group of answer choices
0.48
0.54
0.91
0.76
Flag question: Question 5
Question 53 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?
Group of answer choices
0.023
0.016
0.009
0.005
Flag question: Question 6
Question 63 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?
Group of answer choices
1500
1200
1000
2500
Flag question: Question 7
Question 73 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?
Group of answer choices
1275
35.7
1500
89.5
Flag question: Question 8
Question 83 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?
Group of answer choices
0.0085
0.0025
0.062
0.094
Flag question: Question 9
Question 93 pts
The random variable Y has a Poisson distribution with mean 50. Compute the probability P(Y > 60).
Group of answer choices
0.05
0.09
0.07
0.03
Flag question: Question 10
Question 103 pts
Which of the following statements is TRUE?
Group of answer choices
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 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 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.
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.
Flag question: Question 11
Question 113 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?
Group of answer choices
0.6
0.5
0
0.2
Flag question: Question 12
Question 123 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?
Group of answer choices
6000
6
60
36
Flag question: Question 13
Question 133 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?
Group of answer choices
0.66
0.36
0.72
0.18
Flag question: Question 14
Question 143 pts
When we construct the 99% confidence intervals for the population mean (* denoting a confidence level of 99%), what is the value of Z/2 used in the computation?
Group of answer choices
1.645
2.575
1.96
2.011
Flag question: Question 15
Question 153 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?
Group of answer choices
930.7 ≤ μ ≤ 1069.3
845.2 ≤ μ ≤ 1024.3
975.6 ≤ μ ≤ 1077.3
910.8 ≤ μ ≤ 1055.2
Flag question: Question 16
Question 163 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?
Group of answer choices
21.16 ≤ μ ≤ 38.84
18.40 ≤ μ ≤ 32.97
19.55 ≤ μ ≤ 37.1
19.93 ≤ μ ≤ 35.66
Flag question: Question 17
Question 171 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 H0: = 7725.
Which test is appropriate to apply for this one population hypothesis problem?
Group of answer choices
t test
F test
The maximum likelihood method
Z test
Flag question: Question 18
Question 183 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 H0: = 7725.
What is the value of observed test statistics?
Group of answer choices
-2.82
-1.45
-2.36
-1.76
Flag question: Question 19
Question 193 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 H0: = 7725.
What is the degree of freedom df in this problem?
Group of answer choices
11
8
9
10
Flag question: Question 20
Question 203 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 H0: = 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
2.228
1.96
1.645
2.143
Flag question: Question 21
Question 213 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 H0: = 7725.
What conclusions can be drawn, at the 5% level of significance?
Group of answer choices
The underlying mean daily energy intake is less than 7725 kJ
The underlying mean daily energy intake is not equal to 7725 kJ
The underlying mean daily energy intake is greater than 7725 kJ
The underlying mean daily energy intake is equal to 7725 kJ.
Flag question: Question 22
Question 223 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 ≥ 185 against the alternative hypothesis < 185 at = 0.05.
What is the value of the observed test statistic?
Group of answer choices
-0.78
-0.49
-1.47
-1.22
Flag question: Question 23
Question 233 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 ≥ 185 against the alternative hypothesis < 185 at = 0.05.
What conclusions can be drawn?Group of answer choices
The null hypothesis will be rejected at 5% level of significance
No conclusions can be drawn
More tests need to be carried out
The null hypothesis cannot be rejected at 5% level of significance
Flag question: Question 24
Question 241 pts
Which of the following is not a condition required for comparing means across multiple groups using ANOVA?
Group of answer choices
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.
The data within each group should be nearly normal.
Flag question: Question 25
Question 258 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.
Flag question: Question 26
Question 268 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.
Flag question: Question 27
Question 278 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.
Flag question: Question 28
Question 288 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.
Question 2910 pts
A correlation of -0.92 indicates a __ relationship between X and Y.
Group of answer choices
Strong negative
Weak negative
Strong positive
Weak positive
Flag question: Question 30
Question 3010 pts
The _ is a measure of the strength of the linear relationship between two sets of variables.
Group of answer choices
Coefficient of correlation
Coefficient of determination
ANOVA
Standard error
Flag question: Question 31
Question 3110 pts
The linear regression model is determined by minimizing __.
Group of answer choices
The total squared error between the predicted Y values and the actual Y values
The total error between the X and Y values
The total error between the predicted Y values and the actual Y values
The total squared error between the X and the Y values
Flag question: Question 32
Question 3210 pts
In regression analysis, we can use a _ to visually inspect the data to see whether X and Y are linearly related.
Group of answer choices
Scatter diagram
Pie chart
Time series plot
Boxplot
Flag question: Question 33
Question 3310 pts
The _ is the variable that is being predicted or estimated.
Group of answer choices
Dependent variable
Independent variable
Correlated variable
None of the above
Flag question: Question 34
Question 3410 pts
It is believed that the annual repair cost for the fuel-efficient automobile “ABC” is related to its age. A sample of 10 automobiles revealed the results shown in the table below. Compute the coefficient of correlation.
Y = Repair cost ($) X = Age (years)
170 1
130 1
180 2
205 2
220 3
243 3
290 4
275 4
404 5
380 5
Group of answer choices
0.96
0.77
0.83
-0.84
Flag question: Question 35
Question 3510 pts
It is believed that the annual repair cost for the fuel-efficient automobile “ABC” is related to its age. A sample of 10 automobiles revealed the results shown in the table below. Using the least squares principle, determine the regression equation Y = a + bX
Y = Repair cost ($) X = Age (years)
170 1
130 1
180 2
205 2
220 3
243 3
290 4
275 4
404 5
380 5
Group of answer choices
Y = 77 + 58X
Y = 36 + 49X
Y = 62 - 73X
Y = 80 + 65X
Flag question: Question 36
Question 3610 pts
Many of the parametric methods (e.g. t-test) rely on the assumption that the data are sampled from populations that follows a _ distribution.
Group of answer choices
Normal
Poisson
Uniform
Binomial
Flag question: Question 37
Question 3710 pts
The _ is an appropriate non-parametric technique for comparing two probability distributions when a match-pairs design is used.
Group of answer choices
Wilcoxon signed ranks test
Kruskal-Wallis test
Wilcoxon rank sum test
t test
Flag question: Question 38
Question 3810 pts
Suppose a chi-square test for independence is used to evaluate the relationship between two variables. If one variable is classified into 4 categories and the other variable is classified into 5 categories, then the chi-square statistic will have _.
Group of answer choices
df = 12
df = 20
df = 9
df = 1
Sample Solution