UNIVERSITI TEKNOLOGI MALAYSIA ENGINEERING STATISTICS – SSE/SSCE 2193 2012/2013 SEMESTER I TEST 1 - 15% 1 hour ANSWER ALL QUESTIONS 1. a) An experiment is conducted to select a suitable catalyst for the production of a dispersant for cleaning oil spill in Straits of Malacca. Suppose Ir. Aziz, the chemical engineer randomly selected three catalysts for testing from 10 different proposed catalysts. Four of the catalysts have high acidity level and six of the catalysts have low acidity level. Calculate the probability that not more than one high acidity level catalyst is selected. [4 marks] b) Potholes on a highway can be a serious problem and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that, on the average, 2 potholes per kilometre after a certain amount of usage. It is assumed that the Poisson process applies to the random variable for the number of potholes. i. What is the probability that there will be between 3 and 9 potholes in a given section of 5 km. [2 marks] ii. the What is the probability that there will be more than 3 km section before next pothole is found. [3 marks]

2.

A corporation buys motors for electric fans from company M that guarantees 95% of its motors are nondefective and it will replace all defective motors at no cost. The motors are received in large shipments. Assume that motor selections are independent events. i. What is the probability that the eighth motor selected from a shipment is the third motor found to be defective? [3 marks] ii. The quality control department at the corporation randomly selects 20 motors from each shipment and inspects them for being good or defective. If the sample contains more than two defective motors, the entire shipment is rejected. What is the probability that a given shipment of motors received by the corporation will be rejected. [3 marks]

3.

a) The length of stay for foreign engineering students in Malaysian higher learning...

...Descriptive statistics
information Descriptive statistics organize, summarize, and communicate a group of numerical observations and describe large amounts of data in a single number or in just a few numbers
Inferential statistics
Use samples to draw conclusions about a population Inferential statistical use sample data to make general estimates about the larger population, and infer or make an intelligence guess about, the population
Sample: a set of observations drawn from the population of interest. Samples are used most often because it is rare that we are able to study every person (or organization or laboratory rat) in a particular population.
Researchers usually study a sample, but they are really interested in the population, which includes all possible observations about which we’d like to know something. Discrete Variables that can only take on specific values (e.g., whole numbers) How many letters are in your name?
* Continuous Can take on a full range of values, How tall are you?
Variables are observations of physical, attitudinal, and behavioral characteristics that can take on different values. We use both discrete and continuous numerical observations to quantify variables. Discrete observations can take on only specific values (e.g., whole numbers); no other values can exist between these numbers. Continuous observations can take on a full range of values (e.g., numbers out...

...2nd Exam StudyGuide
Part 1: Terms and Concepts
-Descriptive Statistics: Numbers that, because of their definition and formula, describes certain characteristics or properties of a batch of numbers.
-Central Tendency (all forms): Mean, Median, and Mode. Mean is the sum of all values divided by the number of cases which includes outliers unless calculating a trimmed mean. Median is the middle value when all values are arranged in ascending order. Mode is the value occurring most frequently in a data set.
-Mixed Mode Survey: A mixed mode survey is using multiple survey styles at the same time
-Bivariate Analysis: Bivariate analysis is describing a case in terms of two variables simultaneously. Ex. Attitude toward equality for men and women.
-Content Analysis: The systematic analysis of message characteristics and their inferences by identifying relationships among constructs in the text.
-Filter Question: Questions used to identify relevant respondents.
-Double-Barreled Question: A question that is composed of two different questions. Ex. Do you think George W. Bush should be impeached and exiled to the Galapagos Islands?
-Ethnography: A type of field study in which the researcher is deeply immersed in the place and lives of the people being studied.
-Narrative Analysis: The systematic analysis of message characteristics and their inferences. Used to identify relationships among...

...3
Question 2a 5
Question 2b 6
Question 2c 7
Question 3a 8
Question 3b 8
Question 3c 10
Question 3d 11
Question 4 12
Question 5 14
References 15
Question 1
The sampling method that Mr. Kwok is using is Stratified Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum...

...1. What nursing action is required b4 you measure fundal height= empty bladder full bladder make the fundal height higher.
2. What should a nurse do to prevent heat loss from evaporation= dry them up and remove the wet linen.
3. Child with cephalohematoma. What condition is associated with cephalohemetoma = jaundice
4. Why do we perform gestational age in a baby= to identify developmental level
5. What kind of exam do we perform to access for gestational age = ballot score
6. A baby has been circumcised a mother called the unit and complains that she saw a yellow crust on the penile area what do you tell the mother=Normal
7. You are teaching a mom how to use a bulb syringe what will you tell her to do= tilt babies head to the side and sanction the check
8. You are providing umbilical cord care, what will you do to provide this care= dye, open, dry, to prevent infection.
9. You have a patient who is breast feeding you want to prevent nipple trauma what will you teach= latching on, make sure the oriole is in the baby mouth and the baby is sucking onto it. And the baby is not sucking the nipple.
10. When babies have jaundice and are placed on a phototherapy why should we make sure that they have fluid and they get fed= prevent dehydration, hypoglycemia and promote growth
11. A neonate that was born 4hours after delivery mother is diabetic and some of the signs and symptoms is that the baby is jittery = hypoglycemia, check blood sugar and feed them
12. A woman who...

...AP Statistics Quarter 1 Final (Chapters 1-5)
Chapter 1
Sections 1.1 and 1.2
I. Observation vs. Experiment
A. Observational study: Record data on individuals without attempting to influence the responses. We typically cannot prove anything this way.
B. Experimental study: Deliberately impose a treatment on individuals and record their responses. Influential factors can be controlled.
C. Confounding
1. Two variables (explanatory variables or lurking variables) are confounded when their effects on a response variable cannot be distinguished from each other.
2. Observational studies of the effect of one variable on another often fail because the explanatory variable is confounded with lurking variables.
II. Population vs. Sample
A. Population: The entire group of individuals in which we are interested but can’t usually assess directly
1. A parameter is a number describing a characteristic of the population.
B. Sample: The part of the population we actually examine and for which we do have data
1. A statistic is a number describing a characteristic of a sample.
III. Bad Sampling Methods
A. Convenience sampling: Just ask whoever is around.
B. Voluntary Response Sampling: Individuals choose to be involved. These samples are very susceptible to being biased because different people are motivated to respond or not. They are often called “public opinion polls” and are not considered valid or...

...Key Synthesis/Potential Test Questions (PTQs)
• What is statistics? Making an inference about a population from a
sample.
• What is the logic that allows you to be 95% confident that the confidence interval contains the population parameter?
We know from the CLT that sample means are normally distributed around the real population mean (). Any time you have a sample mean within E (margin of error) of then the confidence interval will contain . Since 95% of the sample means are within E of then 95% of the confidence interval constructed in this way will contain.
• Why do we use confidence intervals verses point estimates? The sample mean is a point estimate (single number estimate) of the population mean – Due to sampling error, we know this is off. Instead, we construct an interval estimate, which takes into account the standard deviation, and sample size.
– Usually stated as (point estimate) ± (margin of error)
• What is meant by a 95% confidence interval? That we are 95% confident that our calculated confidence interval actually contains the true mean.
• What is the logic of a hypothesis test?
“If our sample result is very unlikely under the assumption of the null hypothesis, then the null hypothesis assumption is probably false. Thus, we reject the null hypothesis and infer the alternative hypothesis.”
• What is the logic of using a CI to do a HT?
We are 95% confident the proportion is in this interval… if the sample mean or...

...Chapter 9
Hypothesis Testing
Case Problem 1: Quality Associates, Inc.
1. The hypothesis testing results are shown below:
Sample 1 Sample 2 Sample 3 Sample 4
Sample Size 30 30 30 30
Mean 11.959 12.029 11.889 12.081
Standard Deviation 0.220 0.220 0.207 0.206
Level of Significance (alpha) 0.010 0.010 0.010 0.010
Critical Value (lower tail) -2.576 -2.576 -2.576 -2.576
Critical Value (upper tail) 2.576 2.576 2.576 2.576
Hypothesized value 12 12 12 12
Standard Error 0.040 0.040 0.038 0.038
Test Statistic -1.027 0.713 -2.935 2.161
p-value 0.304 0.476 0.003 0.031
Only sample 3 leads to the rejection of the hypothesis H0: µ = 12. Thus, corrective action is warranted for sample 3. The other samples indicate H0 cannot be rejected and thus from all we can tell, the process is operating satisfactorily. Sample 3 with = 11.89 shows the process is operating below the desired mean. Sample 4 with = 12.08 is on the high side, but the p-value of .03 is not sufficient to reject H0.
2. The sample standard deviations for all four samples are in the .20 to .22 range. It appears that the process population standard deviation assumption of .21 is good.
3. With α = .01, z.005 = 2.576. Using the standard error of the mean =0.0383, the upper and lower control limits are computed as follows:
Upper Control Limit = 12 + 2.576 (0.0383) = 12.0987
Lower Control Limit = 12 - 2.576 (0.0383) = 11.9013
As long as a sample...

...A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample mean to be 100. a.Use an interval estimate to estimate the population mean with 90% confidence.[mu-1.64*SD/√n,mu+1.64*SD/√n] [100-1.64*25/√50,100+1.64*25/√50][94.2017,105.7983]-90% Confidence b.95% confidence. [mu-1.96*SD/√n,mu+1.96*SD/√n] [100-1.96*25/√50,100+1.96*25/√50][93.0704,106.9296]-95% Confidence c.99% confidence. [mu-2.57*SD/√n,mu+2.57*SD/√n] [100-2.57*25/√50,100+2.57*25/√50][90.9137,109.0863]-99% Confidence
The mean of a sample of size n=35 was calculated as xbar=503.4. The sample was randomly drawn from a population with a standard deviation of 15. A researcher wishes to perform the following hypothesis test: H0 :mu500 a.Determine the t-statistic of the above test. Xbar-mu/(SD/√n)=t-statistic 503.4 – 500/(15/√35)=3.4/2.535=1.340978 b.Determine the pvalue of the above test. 1-(Chart of Tstat)=1-.9099=.0901=pvalue c.Suppose a larger sample size n=75, and sample mean remains xbar=503.4 Determine the pvalue of the hypothesis test described above. 503.4 – 500/(15/√75)=3.4/1.732=1.96299 1-.9750=.025=pvalue d.Determine with sample size n=125 503.4 – 500/(15/√125)=3.4/1.3416=2.53421 1-.9943=.0057=pvalue e.Relationship between sample size and pvalue? As sample size increases,pvalue decreses. Inverse relationship.
A medical statistician wants to estimate the average weight loss of...