Business Statistics Assignment -
Quiz 1 -
Question 1 - A study is under way in the Otway National Park to determine the mature height of Mountain Ash gum trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 metres tall. It is estimated that the park contains 25,000 mature Mountain Ash gum trees. The study involves collecting heights from 250 randomly selected mature Mountain Ash gum trees and analysing the results. Identify the population from which the study was sampled.
All Mountain Ash gum trees, of any age, in the park.
The 25,000 mature Mountain Ash gum trees in the park.
The 250 randomly selected mature Mountain Ash gum trees.
All the mature Mountain Ash gum trees taller than 60 metres.
Question 2 - A study is under way in the Otway National Park to determine the mature height of Mountain Ash gum trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 metres tall. It is estimated that the park contains 25,000 mature Mountain Ash gum trees. The study involves collecting heights from 250 randomly selected mature Mountain Ash gum trees and analysing the results. Identify the sample in the study.
The 250 randomly selected mature Mountain Ash gum trees.
The 25,000 mature Mountain Ash gum trees in the park.
All Mountain Ash gum trees, of any age, in the park.
All the mature Mountain Ash gum trees taller than 60 metres.
Question 3 - The data in the Excel file travel work (under Supplementary Material on Canvas site) refer to the distance (in kilometres) that a sample of 50 people drive to work each day.
Using Excel, generate the Descriptive Statistics for the above data.
Note: You are not required to upload the output but to answer the following questions based on the output.
The mean is:
The median is:
The range is:
The IQR is:
The shape of the distribution is:
The most appropriate measure to describe Centre is:
The most appropriate measure to describe Spread is:
Question 4 - The data in the Excel file travel work (under Supplementary Material on Canvas site) refer to the number of kilometres that a sample of 50 people drive to work each day.
Using Excel, construct a histogram to represent the above data. Use a class width of 10 and start the first class at 0.
Note: You are not required to upload the histogram but to answer the following questions based on the histogram.
The shape of the distribution is:
The modality of the distribution is:
Are there any outliers?
Question 5 - True or False: Faculty rank (professor to associate lecturer) is an example of a discrete variable.
True
False
Question 6 - True or False: Whether a university student is a full-fee student or a HECS student is an example of a nominal variable.
True
False
Question 7 - The Crowne Plaza in Canberra's CBD will be open for three meal sittings (breakfast, lunch and dinner) on this year's Christmas day. Due to the extra expense of public holiday rates, the manager does not want to over-staff the restaurant by rostering people on longer than necessary; however they do not want to under-staff the restaurant as they may lose patronage for future events. To assist the manager in preparing the Christmas roster, data were collected randomly over the past 3 months. Consider the data and how to allocate reasonable meal times for the budget considerations.
The file Xmas.xlsx (under Supplementary Material on Canvas site) contains a sample of 1200 dining times, 400 at each meal (in minutes) collected randomly over the past 3 months. Meal sessions are coded Breakfast = 1; Lunch = 2; Dinner = 3.
Construct a side-by-side boxplots for "all meals" and for each of the meal times sessions.
Note: You are not required to upload the side-by-side boxplots but to answer the following questions.
How many potential outliers can be identified in each of the following session?
- All Meals
- Breakfast
- Lunch
- Dinner
Quiz 2a -
Question 1 - An awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they studied on the weekend before the exam, and whether they did well on the exam. Of the 200 students, 100 studied on the weekend before the exam, 110 did well on the exam, and 80 who studied on the weekend before exam did well on the exam.
The probability that a randomly selected student studied on the weekend before the exam or did well on the exam is
0.65
0.15
0.35
0.45
Question 2 - An awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they studied on the weekend before the exam, and whether they did well on the exam. Of the 200 students, 100 studied on the weekend before the exam, 110 did well on the exam, and 80 who studied on the weekend before exam did well on the exam.
The probability that a randomly selected student neither studied on the weekend before the exam nor did well on the exam is
0.35
0.65
0.45
0.15
Question 3 - An awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they studied on the weekend before the exam, and whether they did well on the exam. Of the 200 students, 100 studied on the weekend before the exam, 110 did well on the exam, and 80 who studied on the weekend before exam did well on the exam.
The probability that a randomly selected student did not study on the weekend before the exam but did well on the exam is
0.65
0.35
0.15
0.45
Question 4 - An awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they studied on the weekend before the exam, and whether they did well on the exam. Of the 200 students, 100 studied on the weekend before the exam, 110 did well on the exam, and 80 who studied on the weekend before exam did well on the exam.
The probability that a randomly selected student did not do well on the exam is
0.65
0.15
0.45
0.35
Question 5 - A food processor packages orange juice in small jars. The weights of the filled jars are Normally distributed with a mean of 336 grams and a standard deviation of 9.6 grams.
Find the proportion of all jars packaged by this process that have weights that fall below 348 grams.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.0531
0.1587
0.8944
0.1056
Question 6 - A food processor packages orange juice in small jars. The weights of the filled jars are Normally distributed with a mean of 336 grams and a standard deviation of 9.6 grams.
Find the proportion of all jars packaged by this process that have weights that fall above 345.6 grams.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.1587
0.8944
0.8413
0.0531
Question 7 - A food processor packages orange juice in small jars. The weights of the filled jars are Normally distributed with a mean of 336 grams and a standard deviation of 9.6 grams.
Find the proportion of all jars packaged by this process that have weights between 345.6 grams and 348 grams.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.9469
0.8944
0.0531
0.1587
Question 8 - According to a large company, the probability that their employees have had previous experience if they have had formal training is 45%. Of the employees surveyed, 50% have had previous experience and 40% have had formal training.
The probability that the employees have had formal training if they have had previous experience is
0.56
0.64
0.53
0.36
Question 9 - According to a large company, the probability that their employees have had previous experience if they have had formal training is 45%. Of the employees surveyed, 50% have had previous experience and 40% have had formal training.
The probability that the employees have had previous experience if they have had no formal training is
0.56
0.36
0.47
0.53
Question 10 - According to a large company, the probability that their employees have had previous experience if they have had formal training is 45%. Of the employees surveyed, 50% have had previous experience and 40% have had formal training.
The probability that the employees have had no formal training if they have had no previous experience is
0.44
0.36
0.53
0.56
Quiz 2b -
Question 1 - A recent survey of customer satisfaction for a particular bank revelaed the following outcomes (with their corresponding chance of occurring in brackets): Highly Satisfied (6%), Satisfied (17%), Neutral (18%), Dissatisfied (29%), and Highly Dissatisfied (?). If these are the only outcomes possible for the bank, what is the chance that customers will be Highly Dissatisfied?
6%
14%
22%
30%
Question 2 - True or False: When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B).
True
False
Question 3 - The probability that a new advertising campaign will increase sales is estimated to be 0.60. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.30. Assuming that the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is
0.28
0.32
0.88
0.18
Question 4 - The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had university degrees, 100 were single, and 60 were single university graduates. The probability that an employee of the company is single and does not have a university degree is
0.57
0.63
0.07
0.67
Question 5 - The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will not increase during the next 6 months is
0.75
0.51
0.89
0.25
Question 6 - According to a survey of Australian households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents do not own 2 cars if annual household income is not over $50,000 is
0.12
0.70
0.18
0.45
Question 7 - True or False: The probability that a standard normal random variable, Z, falls between -1.50 and 0.81 is 0.2728.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
True
False
Question 8 - The number of column centimetres of classified advertisements appearing on Mondays in a certain daily newspaper is Normally distributed with a mean of 320 cm and a standard deviation of 20 cm.
Find the probability that on a randomly chosen Monday there will be less than 340 column centimetres of classified advertisement.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.8413
0.0668
0.1587
0.9544
Question 9 - The number of column centimetres of classified advertisements appearing on Mondays in a certain daily newspaper is Normally distributed with a mean of 320 cm and a standard deviation of 20 cm.
Find the probability that on a randomly chosen Monday there will be more than 350 column centimetres of classified advertisement.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.9544
0.0668
0.9332
0.8413
Question 10 - If we know that the length of time it takes a university student to find a parking space in the university car park follows a Normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute.
Find the probability that a randomly selected university student will take between 2 and 4.5 minutes to find a parking space in the car park.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.0919
0.4938
0.7745
0.2255
Quiz 3 -
Question 1 - The quality control manager at a light globe factory needs to estimate the mean life of a large shipment of energy-saving light-emitting diode (LED) light globes. The standard deviation is known to be 3 months. A random sample of 64 light globes indicates a mean life of 34 months.
Which of the following is the correct 95% confidence interval for the population mean life of light globes in this shipment.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
(28.12, 39.88)
(31, 37)
(33.27, 34.74)
Question 2 - Water resources in many parts of many parts of Australia are being closely watched and restrictions have been imposed of activities such as garden watering. Suppose that ACT Water monitors water usage in a suburb and finds that for one summer the average household usage is 408 litres a day. A year later it examines records of a sample of 50 households and finds that there is a daily mean usage of 380 litres with a standard deviation of 25 litres.
Which of the following is the correct 90% confidence interval for the population mean daily water usage in the second summer.
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
(374.07, 385.93)
(355, 405)
(338.09, 421.92)
Question 3 - A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when the mean amount dispensed is 330mL. The standard deviation of the amount dispensed is known to be 4mL. A random sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 330mL. Suppose that the mean amount dispensed in a particular sample of 50 bottles is 329.7mL.
Is there evidence that the filling line has to be stopped, at the 10% significance level?
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
The population parameter of interest is
The null hypothesis is
The alternative hypothesis is
The level of significance is
The test statistic is
The p-value is
The decision is
Based on the sample, there is
Question 4 - A chocolate manufacturer uses machines to pack chocolates. Although the packages are labelled as 225 gm, the company wants the packages to contain 230 gm so that virtually none of the packages contain less than 225 gm. A random sample of 50 packages is selected periodically and the packaging process is stopped if there is evidence that the mean amount packaged is different from 230 gm. Suppose that the mean amount packaged in a particular sample of 50 packages is 230.6 gm with a standard deviation of 1.45 gm.
Is there evidence that the mean amount packaged is different from 230 gm, at the 1% significance level?
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
The population parameter of interest is
The null hypothesis is
The alternative hypothesis is
The level of significance is
The test statistic is
The p-value is
The decision is
Based on the sample, there is
Question 5 - It is important to monitor traffic on a website as organisations need to obtain information about online interactions with their clients. For example, businesses applying for an Australian Business Number (ABN) online are asked at the end of the process how long it has taken. Assume that the ABN online application times are normally distributed with a mean time of 40 minutes and a standard deviation of 5 minutes.
If a random sample of 50 applications is taken, what is the probability that the sample mean is between 39 and 41 minutes?
Note: All intermediate calculations must be reported to 4 decimal places before performing the final calculation.
0.0787
0.9213
0.8426
0.1574
Attachment:- Data Files.rar