ECO541-Assignment 1 - Assignment 1 PDF

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FACULTY OF BUSINESS AND MANAGEMENTBACHELOR OF BUSINESS ADMINISTRATION (HONS)BUSINESS ECONOMICS AND BACHELOR OF SCIENCE(HONS) MANAGEMENT MATHEMATICS (BA290)BA 2502ASTATISTICAL METHODSECO 541ASSIGNMENT 1PREPARED FOR:DR CHUAH SOO CHENGPREPARED BY:AINI AQILAH BINTI ADNAN (2020352131)DATE OF SUBMISSION14...

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FACULTY OF BUSINESS AND MANAGEMENT BACHELOR OF BUSINESS ADMINISTRATION (HONS) BUSINESS ECONOMICS AND BACHELOR OF SCIENCE (HONS) MANAGEMENT MATHEMATICS (BA290) BA 2502A STATISTICAL METHODS ECO 541

ASSIGNMENT 1

PREPARED FOR: DR CHUAH SOO CHENG

PREPARED BY: AINI AQILAH BINTI ADNAN (2020352131)

DATE OF SUBMISSION 14 NOVEMBER 2020

QUESTION 1 a) Indicate which of the following variable are quantitative and which are qualitative and classify the quantitative variables as discrete or continuous. i.

The amount of time a student spent studying for an exam. (Discrete Quantitative)

ii.

The amount of rain last year in 30 cities. (Continuous Quantitative)

iii. The arrival status of an airline flight (early, on time, canceled) at an airport. (Qualitative) iv. A person’s blood type. (Qualitative) v.

The amount of gasoline put into a car at a petrol station. (Continuous Quantitative)

b) What is the level of measurement for each of the following variables? i) Student IQ ratings. (Ordinal) ii) Distance students travel to class. (Ratio) iii) The jersey numbers of a sorority soccer team. (Interval) iv) A classification of students by state or birth. (Nominal) v) A summary of students by academic class – that is, freshman, sophomore, junior, and senior. (Ordinal)

c) Prepare a box-and-whisker plot for the following data: 11 8 26 31 62 19 7 3 4 75 33 30 42 15 18 23 29 13 16 6 Comment on the skewness of these data. Does this data set contain any outliers? 1)

Minimum: 3

2)

Q1: 8.75

3)

Median (Q2):

4)

Q3: 30.75

5)

Maximum: 75

471 = 23.55 20

Comment: The distribution is skewed to the left and there is an outlier because the point are outside the upper inner fence.

QUESTION 2 a) The pucks used by the National Hockey League for ice hockey must eight between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.75 ounces and a standard deviation of 0.11 ounce. What percentage of the pucks produced at this factory cannot be used by the National Hockey League?

  5.75   0.11 p (5.5  x  6.0) 5.5  5.75 6.0  5.75 z  p( ) 0.11 0.11  p (2.27  z  2.27)  0.9884  0.0016  0.9768 1 0.9768  0.0232  2.32% b) Ashley knows that the time it takes her to commute to work is approximately normally distributed with a mean of 45 minutes and a standard deviation of 3 minutes. What time must she leave home in the morning so that she is 95% sure of arriving at work by 9 a.m.?

  45  3 z  95%  0.95  1.64 x  z  x  45 1.64  3 x  49.92  0.832hours 9 hours  0.832 hours  8.17 a.m. 

She should leave at 8.17 a.m. so that she can arrive at work by 9 a.m.

c) The management at Ohio National Bank does not want its customers to wait on line for service for too long. The manager of a branch of this bank estimated that the customer currently have to wait an average of 8 minutes for service. Assume that the waiting times for all customers at this branch have a normally distribution with a mean of 8 minutes and a standard deviation of 2 minutes. i) What percentage of the customers have to wait for 10 to 13 minutes?

 8  2 p (10  x  13) 10  8 13  8  p(  z ) 2 2  p (1  z  2.5)  0.9938 0.8413  0.1525  15.25% ii) Is it possible that a customer may have to wait longer than 16 minutes for services? Explain.

p ( x  16) 16  8 ) 2  p ( z  4) 1  p( z 



Possible because there is a possibility that a customer may have to wait longer than 16 minutes for services.

QUESTION 3 a) A machine at Katz Steel Corporation makes 3-inch-long mails. The probability distribution of the lengths of these nails is normal with a mean of 3 inches and a standard deviation of 0.1 inch. The quality control inspector takes a sample of 25 nails one a week and calculates the mean length of these nails. If the mean of this sample is either less than 2.95 inches or greater than 3.05 inches, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment?

 3   0.1 n  25 0.1    0.02 n 25 p (2.95  x  3.05) 2.95  3 3.05  3  p(  z ) 0.02 0.02  p (2.5  z  2.5)  0.9938  0.0062  0.9876

b) Among college students who hold part-time jobs during the school year, the distribution of time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week for 18 randomly selected college students who hold part-time jobs during the school year is

i) Not within 1 hour of the population mean

  20.20   2.60 n  18 2.6    0.61 n 18 p ( 1 x  1) 1 1 )  p( z 0.61 0.61  p (1.64  z  1.64)  0.9495 0.0505  0.8990 1  8.8990  0.101 ii) 20 to 20.50 hours

  20.20   2.60 n  18 2.6    0.61 n 18 p (20  x  20.50) 20  20.20 20  20.50  p(  z ) 0.61 0.61  p(0.33  z  0.49)  0.6879 0.3707  0.3172

iii) At least 22 hours

  20.20   2.60 n  18 2.6    0.61 18 n p( x  22) 22  20.20 ) 0.61  p ( z  2.95)  0.9984  p( z 

1  0.9984  0.0016 iv) No more than 21 hours

  20.20   2.60 n  18 2.6    0.61 18 n p( x  21) 21 20.20 ) 0.61  p ( z  1.31)  0.9049  p( z 

1  0.9049  0.0951

c) The Quality Assurance Department for Cola Inc. maintains records regarding the amount of cola n its Jumbo bottle. The actual amount of cola in each bottle is critical, but varies a small amount from one bottle to the next. Cola Inc. does not wish to under fill the bottles, because it will have a problem with truth in labeling. On the other hand, it cannot overfill each bottle, because it would be giving cola away, hence reducing its profits. Its records indicate that the amount of cola follows the normally distribution. The mean amount per bottle is 31.2 ounces and the population standard deviation is 0.4 ounces. The quality technician randomly selected 16 bottles from the filling line. The mean amount of cola contained in the bottles is 31.38 ounces. Is this an unlikely result? Is it likely the process is putting too much soda in the bottles? To put in another way, is the sampling error pf 0.18 ounces unusual?

  31.2   0.4 n  16   0.18 n z

x 

 n 31.38  31.20 z 0.4 16 0.18 z 0.1  1.8  0.9641  96.41% 

Due to the higher percentage of Cola with an even percentage of soda, the process is acceptable. No, the sampling error of 0.18 ounces is not unusual....