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business statistics using excel
Basic Business Statistics Concepts And Applications 5th Edition L. Berenson Mark, David Levine, Kathryn Szabat, Judith Watson, Nicola Jayne, Martin O'brien - Solutions
A manufacturer of batteries claims that its products last longer than those of its competitors. The following information measures the lifetime of the manufacturer’s batteries versus those of its competitors (in minutes).
An article appearing in The Exponent, an independent college newspaper published by the Purdue Student Publishing Foundation, reported that the average American college student spends 1 hour (60 minutes) on Facebook daily (data obtained from ). You wonder if there is a difference between males and
Do people in the Campbelltown area pay higher petrol prices than those in the rest of Sydney? Data reported by Valadkhani(Energy Economics, 39, September 2013, 66–80) show a mean petrol price of 140.1c per litre and standard deviation of 12.1 for Campbelltown from a sample of 223 weeks of data
Nutrition Australia’s website states: ‘A lot of publicity has been given to a wide variety of diets lately. Some of these advocate high protein intake, some stress carbohydrate, others seem to be intermediate. What are these diets supposed to achieve, and what, if any, is the scientific
Do private school students obtain higher marks than public school students? To evaluate this question we collected a sample of Australian Tertiary Admission Rank (ATAR) data from 2014. We obtained a mean ATAR of 76.5 with a standard deviation of 12 from a sample of 54 private school students. A
When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this
Referring to problem 10.4, construct a 95% confidence interval estimate of the population difference between μ1 and μ2.
What assumptions about the two populations are necessary in problem 10.4?
You need to test whether the average mealtime spending of American tourists (population 1) is greater than that for British tourists (population 2). Based on samples of 20 American tourists(n1 = 20) and 17 British tourists (n2 = 17), you calculated the following statistics: X–1 = $53, S1 = $4,
What is the p-value in problem 10.1 if you are testing H0: μ1 - μ2 = 0 against the two-tail alternative H1: μ1 - μ2 Z 0?
What is your decision in problem 10.1 if you are testing H0: μ1 - μ2 = 0 against the two-tail alternative H1: μ1 - μ2 Z 0 using a level of significance of α = 0.10?
Given a sample of n1 = 30 from a population with known standard deviation σ1 = 10, and an independent sample of n2 = 30 from another population with known standard deviation σ2 = 15, what is the value of the Z test statistic for testing H0: μ1 = μ2 if mean X–1 = 72 and X–2 = 66?
Referring to the results of problem 9.96 concerning ‘Bondi’ and‘Vincentia’ shingles, write a report that evaluates the particle loss of the two types of shingles.
The owner of a specialty coffee shop wants to study the coffee-purchasing habits of customers at her shop. During a certain week, she selects a random sample of 160, with the following results:• the amount spent was X _5 $10.25, S 5 $2.75• 84 customers say they ‘definitely will’ recommend
Financial institutions utilise prediction models to predict bankruptcy. One such model is the Altman Z score model, which uses multiple corporate income and balance sheet values to measure the financial health of a company. If the model predicts a low Z score value, the company is in financial
In hypothesis testing, the common level of significance is a 5 0.05. Some might argue for a level of significance greater than 0.05. Suppose that web designers tested the proportion of potential web page visitors with a preference for a new web design over the existing one. The null hypothesis was
The manufacturer of ‘Bondi’ and ‘Vincentia’ terracotta roof shingles provides its customers with a 50-year warranty on most of its products. To determine whether a shingle will last as long as the warranty period, accelerated-life testing is conducted at the manufacturing plant.
A manufacturer of women’s tracksuits needs to check that the average height of 18–25-year-old female athletes is still 1,700 mm. The company collects measurements of 30 basketball players of this age. They are shown in the file< HEIGHTS > and below:
A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon to 1 pm lunch period. The waiting time (defined as the time from when customers join the queue until they reach the teller’s window) of all customers during this hour
A private health fund auditor is assigned the task of evaluating benefits paid to members for dental consultation claims. The audit is conducted on a sample of 85 claims.• In 10 of the consultations, an incorrect amount of reimbursement was provided.• The amount of benefit was: X _5 $98.95, S 5
The owner of a petrol station wants to study petrol-purchasing habits by motorists at his station. He selects a random sample of 60 motorists during a certain week with the following results:• Amount purchased: X _5 42.8 litres, S 11.7 litres.• 11 motorists purchased premium unleaded
For the March quarter 2017, it has been reported that the bulk-billing rate under Medicare for all Medicare Benefits Schedule (MBS) services was 78.7% (Australian Government, Department of Health, Quarterly Medicare Statistics Suppose the government proposes to make changes to scheduled fees and
TasmanTrading, a company developing resorts in holiday areas along the east coast of Australia, has developed an econometric model to help predict the profitability of sites that are being considered as locations for new resort projects. If the model predicts large profits, the company buys the
Your company is carrying out tests on a new pharmaceutical product which has the potential to treat a serious disease.From a sample of 250 persons in the trial, 162 report improvement in their symptoms over a three-month period. You wish to carry out a test to see if the population proportion
In planning to carry out a test of hypothesis based on a designed experiment or research study under investigation, what are some of the questions that you need to raise to ensure that proper methodology will be used?
What are some of the ethical issues to be concerned about when performing a hypothesis test?
What is the six-step critical value approach to hypothesis testing?
How can a confidence interval estimate for the population mean provide conclusions to the corresponding hypothesis test for the population mean?
What is meant by a p-value?
What is the difference between a one-tail and a two-tail test?
What is meant by the power of a test?
What is the difference between a Type I and a Type II error?
What is the difference between a null hypothesis, H0, and an alternative hypothesis, H1?
A supermarket chain wants to test a hypothesis about the average amount spent per week on fruit and vegetables by customers across Australia.a. Using the questions listed in Section 9.7 as a guide, design a method of collecting data and describe an appropriate hypothesis-testing method the
as a guide, design a method of collecting data and describe the hypothesis test the department will use for its test.b. What ethical issues might the department encounter?
A government department wishes to carry out a study to find the proportion of all 15-year-old teenagers who smoke at least once each week.a. Using the questions listed in Section
You wish to carry out research then test a hypothesis about the average hours of employment undertaken by full-time university students during semester.a. Using the questions listed in Section 9.7 as a guide, design the method of collecting data and describe the hypothesis test you will use.b. How
Refer to problem 9.73. If the operations manager stops the process when there is sufficient evidence that the mean life is different from 40,000 km (either less than or greater than) and a random sample of 100 tyres is selected together with a level of significance of a 5 0.05, calculate the power
Refer to problem 9.73. If you select a random sample of 25 tyres and are willing to have an a risk of committing a Type I error, calculate the power of the test and the probability of a Type II error (β) if the population mean life is actually:a. 38,400 kmb. 39,840 kmc. Compare the results in
Refer to problem 9.73. If you are willing to have an a 5 0.01 risk of committing a Type I error, calculate the power of the test and the probability of a Type II error (β) if the population mean life is actually:a. 38,400 kmb. 39,840 kmc. Compare the results in (a) and (b) of this problem and
A tyre manufacturer produces tyres that have a mean life of at least 40,000 km when the production process is working properly.Based on past experience, the standard deviation of the tyres is 5,600 km. The operations manager stops the production process if there is sufficient evidence that the mean
Refer to problem 9.70. If you select a random sample of 25 cups and are willing to have an 0.05 risk of committing a Type I error, calculate the power of the test and the probability of a Type II error (β) if the population mean amount dispensed is actually:a. 197 mL per cupb. 194 mL per cupc.
Refer to problem 9.70. If you are willing to have an a 5 0.01 risk of committing a Type I error, calculate the power of the test and the probability of a Type II error (b) if the population mean amount dispensed is actually:a. 197 mL per cupb. 194 mL per cupc. Compare the results in (a) and (b) of
A coin-operated soft-drink machine is designed to discharge at least 200 mL of drink per cup with a standard deviation of 6 mL. If you select a random sample of 16 cups and you are willing to have an a 0.05 risk of committing a Type I error, calculate the power of the test and the probability of a
The QILT 2016 Graduate Outcomes Survey found that 70.9% of undergraduates had found full-time work within four months of completing their degrees (). Now imagine that a researcher carries out a follow-up study by surveying a representative sample of 1,000 recent graduates from undergraduate degree
The Australian Bureau of Statistics reported that, for the year 2015–16, 38.2% of businesses had a social media presence(Australian Bureau of Statistics, Business Use of Information Technology, 2015–16, Cat. No. 8129.0). Assume a recent survey has been carried out of 3,996 Australian businesses
The Environmental Protection Authority in New South Wales published a paper which discussed plastic shopping bags. The paper referred to a 2015 Omnipoll survey which showed 64%of NSW respondents supported a total ban on single-use plastic shopping bags (Environmental Protection Authority, Plastic
The ABS reported that 30.6% of those who were unemployed at June 2017 were looking for only part-time work (Australian Bureau of Statistics, Labour Force, Australia, DetailedElectronic Delivery Cat. No. 6291.0.55.001, June 2017). Assume that at a later date 975 unemployed people are interviewed and
Assume that an article in a weekend newspaper implies that more than half of all Sydney residents would prefer tolls on all motorways to be reduced by 25 cents, rather than receiving a$100 lower annual registration cost for their cars. Also assume that this was based on a telephone poll where 593
and you choose the level of significance of a 5 0.05. What is your statistical decision?
against the two-tail alternative hypothesis H1: π Z
In problems 9.62 and 9.63, suppose you are testing the null hypothesis H0: π 5
In problem 9.62, if the null hypothesis is that 20% of the items in the population are defective, what is the value of the Z test statistic?
If, in a random sample of 400 items, 88 are defective, what is the sample proportion of defective items?
Suppose the following table contains a random sample of a one-day change in value of 30 managed funds as reported in a financial newspaper. < CHANGE >
One operation of a steel mill is to cut pieces of steel into parts that are used in the frame for front seats in a car. The steel is cut with a diamond saw and the resulting parts must be within 60.125 mm of the length specified by the car manufacturer.The data in the file < STEEL > come from a
Assume that the quality control section of a company that produces chemical products has tested a number of batches for viscosity (resistance to flow). The level of viscosity is an important indicator of the quality of products such as inks, oils and resins. The data for 120 batches are in the data
At a large furniture and electrical store customers usually find that the furniture on display is not held in stock.Rather than being immediately available it must be sourced from manufacturers. In the sofa department the average delivery time is expected to be six weeks after purchase. In order to
The following data represent the amount of soft drink in a sample of 50 consecutive 2-litre bottles. < DRINK > The results are listed horizontally in the order of bottles being filled:
The approval process for a life insurance policy requires a review of the application and the applicant’s medical history, possible requests for additional medical information and medical examinations, and a policy compilation stage where the policy pages are generated then delivered. The ability
A manufacturer of chocolate-coated sweets uses machines to package the sweets as they move along a filling line. Although the packages are labelled as 250 g, the company wants the packages to contain 250.4 g so that virtually none of the packages contains less than 250 g. A sample of 50 packages is
minutes with a sample standard deviation of 0.8 minutes. At the 0.05 level of significance, is there sufficient evidence that the population mean waiting time is now less tha 3.7-.- minutes?
You are the manager of a fast-food franchise. Last month the mean waiting time at the counter, as measured from the time a customer places an order until the time the customer receives the order, was 3.7 minutes. The franchise helped you to institute a new process intended to reduce waiting time.
A large supermarket chain has a target average waiting time of 90 seconds for customers who queue to use the self-service checkouts. To test that a particular store is meeting this target, the waiting time for a random sample of 50 customers in this queue is recorded during a one-day trading
The director of admissions at a large university advises parents of incoming students about the cost of textbooks during a typical semester. He selected a sample of 100 students and recorded their textbook expenses for the semester. He then calculated a sample mean cost of $675.60 and a sample
In a sample of n 5 160 selected from a left-skewed population, X _5 65 and S 5 21. Would you use the t test to test the null hypothesis, H0: m 5 60? Discuss.
In a sample of n 5 16 selected from a left-skewed population, X _5 65 and S 5 21. Would you use the t test to test the null hypothesis, H0: m 5 60? Discuss.
In problems 9.46, 9.47 and 9.48, what is your statistical decision if the alternative hypothesis, H1, is:a. m Z 50?b. m . 50?
In problems 9.46 and 9.47, what are the critical values from the t table if the level of significance a 5 0.05 and the alternative hypothesis H1 is:a. m Z 50?b. m . 50?
In problem 9.46, how many degrees of freedom are there in the one-sample t test?
In a sample of n 5 16 selected from a normal population, X _5 56 and S 5 12. What is the value of the t test statistic if you are testing the null hypothesis, H0: m 5 50?
A New Zealand researcher believes that, on average, teenagers aged 16–19 living in a major city will post photographs on social network sites more than 10 times a week. Suppose she wishes to find statistical evidence to support this. Let m represent the population mean number of times
level of significance, is there sufficient evidence that the mean delivery time has been reduced below the previous value of 25 minutes?b. At the 0.05 level of significance, use the five-step p-value approach.c. Interpret the meaning of the p-value in (b).d. Compare your conclusions in (a) and (b).
minutes.a. Using the six-step critical value approach, at the
You are the manager of a restaurant that delivers pizza to customers. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. From past experience, you can assume that the population standard
level of significance, what decision would you make using the p-value approach to hypothesis testing?c. Interpret the meaning of the p-value in this problem.d. Compare your conclusions in (a) and (b).
level of significance, what decision would you make using the critical value approach to hypothesis testing?b. If you want to test the hypothesis at the
The Glendale Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars with a mean length of at least 855 mm and a standard deviation of 65 mm (as determined from engineering specifications on the production equipment involved). Longer steel bars
In problem 9.41, what is the statistical decision if you tested the null hypothesis at the 0.01 level of significance?
In a lower-tail hypothesis test where you reject H0, you calculate the value of the test statistic Z as 11.38. What is the p-value?
In problem 9.39, what is your statistical decision if you tested the null hypothesis at the 0.01 level of significance?
Suppose that, in a lower-tail hypothesis test where you reject H0, you calculate the value of the test statistic Z as 21.38.What is the p-value?
In problem 9.37, what is your statistical decision if you tested the null hypothesis at the 0.05 level of significance?
Suppose that, in an upper-tail hypothesis test where you reject H0, you calculate the value of the test statistic Z to be 12.00.What is the p-value?
In problem 9.35, what is your statistical decision if the calculated value of the Z test statistic is 21.15?
What is the lower-tail critical value of the Z test statistic at the 0.01 level of significance?
In problem 9.33, what is your statistical decision if the calculated value of the Z test statistic is 12.39?
What is the upper-tail critical value of the Z test statistic at the 0.01 level of significance?
The owner of an ATM machine located inside a petrol station will earn more from fees if customers withdraw money more often rather than taking out large withdrawals less frequently.The owner is interested in checking whether the average withdrawal amount in this location is still $80 with a
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 330 mL. The population standard deviation of the amount dispensed is 4 mL. A sample
The inspection division of a state department that regulates trade measurement is interested in determining whether the proper amount of soft drink has been placed in 2-litre bottles at the local bottling plant of a large, nationally known soft-drink company. The bottling plant has informed the
The quality-control manager at a factory that manufactures memory cards for digital cameras needs to determine whether a large shipment of UHS cards has a mean write speed equal to 90 MB per second. The population standard deviation is 8 MB/s. A random sample of 64 cards indicates a sample mean
The director of manufacturing at a fabric mill needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth should have a mean breaking strength of 30 kg and a standard deviation of 3.5 kg. A sample
In problem 9.26, what is your statistical decision if you test the null hypothesis at the 0.01 level of significance?
Suppose that in a two-tail hypothesis test you calculate the value of the test statistic Z as 21.38. What is the p-value?
In problem 9.24, what is your statistical decision if you test the null hypothesis at the 0.10 level of significance?
Suppose that in a two-tail hypothesis test you calculate the value of the test statistic Z as 12.00. What is the p-value?
What is your decision in problem 9.22 if the calculated value of the test statistic Z is 22.61?
If you use a 0.01 level of significance in a (two-tail) hypothesis test, what is your decision rule for rejecting H0: m 5 12.5 if you use the Z test?
If you use a 0.10 level of significance in a (two-tail) hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean is 500 if you use the Z test?
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