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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
If you use a 0.05 level of significance in a (two-tail) hypothesis test, what will you decide if the calculated value of the test statistic Z is 12.21?
The quality-control manager at a factory that manufactures lithium batteries needs to determine whether they are performing to specification. Their mean runtime before recharging is required to be 10 hours. It is known that the population standard deviation is 0.25 hours. A random sample of 64
The manager of a paint supply store wants to determine whether the amount of paint contained in 4-litre cans purchased from a nationally known manufacturer actually averages 4 litres. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.12
The director of manufacturing at a textile 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 40 kilograms. A sample of 49 pieces of cloth
As a result of complaints from both students and teaching staff about the timetable, the registrar at a large university wants to adjust the scheduled class times to allow for adequate travel time between classes and is ready to undertake a study. Until now, the registrar has believed that 10
The process of deciding which drugs are effective and which may in fact do harm falls in the United States to the Food and Drug Administration (FDA). In April 2017 it wrote warning letters to 14 US companies who were selling products that fraudulently claim to prevent, treat or cure cancer. It is
is presumed guilty until proven innocent, as in some other judicial systems. How do the null and alternative hypotheses differ from those in problem 9.13? What are the possible consequences of committing either a Type I or a Type II error here?
Suppose the defendant in problem
In the Australian legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, H0, that the defendant is innocent, and an alternative hypothesis, H1, that the defendant is guilty. A jury has two possible decisions:convict the defendant (i.e. reject the null
For H0: m 5 100, H1: m Z 100, and for a sample of size n, why is β larger if the actual value of m is 90 than if the actual value of m is 75?
For a given sample size, if a is reduced from 0.05 to 0.01, what will happen to β?
Why is it possible not to reject the null hypothesis when it is false?
Why is it possible to reject the null hypothesis when in fact it is true?
How is the power related to the probability of making a Type II error?
What is the relationship of β to the Type II error?
What is the relationship of a to the Type I error?
What does 1 2 β represent?
What symbol do you use for the chance of committing a Type II error?
What symbol do you use for the level of significance or chance of committing a Type I error?
You use the symbol H1 for which hypothesis?
You use the symbol H0 for which hypothesis?
Referring to the results in problem 8.77 concerning the width of a steel trough, write a report that summarises your conclusions.
Diners have rated 14 North Island and 14 South Island New Zealand restaurants on the basis of food, presentation, service and toilets using an online review system with ratings from 1 to 10. The data file < REST_NZ > contains the ratings for each of these categories.For each island separately:a.
The manufacturer of ‘Bondi’ and ‘Vincentia’ terracotta roof shingles provides its customers with a 50-year warranty on the product. To determine whether a shingle will last as long as the warranty period, accelerated life testing is conducted at the manufacturing plant. Accelerated life
A busy landscaping supplies company sells wood chips for garden mulch. The mulch is sold by the cubic metre and delivered to households in a small truck. Each truckload is expected to be 4 cubic metres. The company decides to conduct an audit of actual load volumes by smoothing and measuring
A manufacturing company produces steel housings for electrical equipment. The main component of the housing is a steel trough made out of a 2-mm steel coil. It is produced using a 250-tonne progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make
A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount of tea in a bag is 5.5 g. If the bags are underfilled, two problems arise. First, customers may not be
A large computer store is conducting an end-of-month inventory of the tablet computers in stock. An auditor for the store wants to estimate the mean value of the tablets in stock at that time. He wants to have 99% confidence that his estimate of the mean value is correct to within ±$23. On the
An auditor for a government agency needs to evaluate payments that were made by Medicare for consultations in doctors’surgeries in a particular postcode area during June. A total of 25,056 visits occurred during June in this area. The auditor wants to estimate the total amount paid by Medicare to
An auditor needs to estimate the percentage of times a company fails to follow an internal control procedure. A sample of 50 from a population of 1,000 items is selected, and in 7 instances the internal control procedure was not followed.a. Construct a 90% one-sided confidence interval estimate of
The manufacturer of Tuffstuff concrete pavers claims its products have a breaking strength of 5 kN. A representative of a building advisory organisation is interested in assessing this claim and sends a number of pavers to be tested in a laboratory. The representative wants to know with
The owner of a restaurant that serves continental food wants to study the characteristics of his customers. He decides to focus on two variables: the amount of money spent per diner on food and whether diners order dessert. The results from a sample of 60 diners are as follows:• amount spent:
The branch manager of an outlet (store 1) of a nationwide chain of pet supply stores wants to study the characteristics of her customers. In particular, she decides to focus on two variables: the amount of money spent by customers and whether the customers own only one dog, only one cat, or more
A survey of Internet shopping for goods looked at how much shoppers spent on online purchases of clothing, footwear and accessories in the past year. The results from a sample of 270 customers are as follows:• amount spent: X– $528.90 S = $113.90• 108 customers stated that they made the
The market research manager for Dalton’s department store wants to study women’s spending on cosmetics. A survey is designed to estimate the proportion of women who purchase their cosmetics primarily from Dalton’s department store, and the mean yearly amount that women spend on cosmetics. A
The personnel manager of a large corporation wishes to study absenteeism among clerical workers at the corporation’s central office during the year. A random sample of 25 clerical workers reveals the following:• absenteeism: X– = 9.7 days, S = 4.0 days• 12 clerical workers were absent for
A researcher for a state government agriculture department wants to study various characteristics of medium-sized farms in the state. A random sample of 70 farms of between 100 and 600 hectares reveals the following:• average area X– = 350 hectares, standard deviation S = 70 hectares• 21
A study by the Australian Bureau of Statistics looked at health and activity habits of various groups of Australians. It found that only 43.3 % of males aged 35–44 had participated in sufficient physical activity in the last week for health purposes. It also found that males of all ages spent an
The Legal Services Council conducted a consumer survey in 2017 which asked respondents about different attitudes and experiences relating to legal costs. One question asked: ‘How well did you understand what the costs were likely to be?’(Legal Services Council Consumer Survey 2017 ( accessed 6
The KPMG 2016 report, Global Profiles of the Fraudster gives details of a survey of investigations between March 2013 and August 2015 relating to frauds committed by 750 people worldwide. Where fraudsters were working in collaboration with others, the most common means of detection were tipoffs and
In 2014–15 the Australian Bureau of Statistics conducted a multipurpose household survey and had responses from 13,686 individuals in private dwellings on their use of information technology. Assume there were 477 15–17 year old respondents and 2,256 45–54 year old respondents who used the
A trade union of medical workers conducted a survey through its website about preferred working hours. Hospital workers visiting the website were given the opportunity to fill out an on-screen survey form. A total of 665 workers responded to a question that asked whether they would prefer a
How does difference estimation differ from estimating the mean?
When would you want to estimate the population total instead of the population mean?
Under what circumstances do you use a one-sided confidence interval instead of a two-sided confidence interval?
Why is it true that, for a given sample size n, an increase in confidence is achieved by widening (and making less precise)the confidence interval?
When do you use the t distribution to develop the confidence interval estimate for the mean?
Why is it that you can never really have 100% confidence of correctly estimating the population characteristic of interest?
The Snowy Ski Centre Pty Ltd conducts an annual audit of its financial records. An internal control policy for the company is that a cheque can be issued only after the accounts payable manager initials the invoice. The tolerable exception rate for this internal control is 0.04. During an audit, a
Econe Pty Ltd is a small company that manufactures women’s dresses for sale to specialty stores. There are 1,200 inventory items, and the historical cost is recorded on a first in, first out(FIFO) basis. In the past, approximately 15% of the inventory items were incorrectly priced. However, any
When a trade discount is allowed by wholesalers for particular types of early payments by customers, the Goods and Services
A branch of a chain of large electronics stores is conducting an end-of-month inventory of the merchandise in stock. There are 1,546 items in inventory at the time. A sample of 50 items is randomly selected and an audit conducted, with the following results:Value of merchandise X = $252.28 S =
The personnel department of a large corporation employing 3,000 workers wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in dollars) for the
A stationery store wants to estimate the total retail value of the 300 greeting cards it has in its inventory. Construct a 95%confidence interval estimate of the population total value of all greeting cards that are in the inventory if a random sample of 20 greeting cards indicates an average value
If p = 0.04, n = 300 and N = 5,000, calculate the upper bound for a one-sided confidence interval estimate of the population proportion, π, using a level of confidence of:a. 90%b. 95%c. 99%
Suppose that a sample of 200 is selected from a population of 10,000 items. Ten items are found to have errors of the following amounts:
and the sample standard deviation is 7.8.Construct a 99% confidence interval estimate of the population total.
A sample of 25 is selected from a population of 500 items. The sample mean is
A study conducted by the Australian Securities Exchange found that 36% of 4,009 Australian adults surveyed in late 2014 held shares, either directly or indirectly through unlisted managed funds (Australian Securities Exchange, 2014 Australian Share Ownership Study, accessed 5 July 2017).a.
Suppose that a survey of the audience at a Sydney Symphony Orchestra (SSO) concert has found that 48 out of 350 members of the audience who participated in the survey are visitors to Sydney.a. Construct a 95% confidence interval for the population proportion of audience members at SSO concerts who
The Nielsen company regularly conducts research into consumer purchases. Neilsen Homescan data for the 52 weeks ended 28 January 2017 showed that 34.5% of Australian homes had purchased Asian vegetables in that period. Households of 1–2 persons accounted for 47% of the volume in Asian vegetable
At a large South East Asian airport flights are classified as being‘on time’ if they land less than 15 minutes after the scheduled time. A study of airlines using the airport finds that one of the airlines that services Australia has a record of 17% of flights arriving late. Suppose you were
Suppose that an energy company wants to estimate its mean waiting time for natural gas installation to within ±5 days with 95% confidence. The company does not have access to previous data, but suspects that the standard deviation is approximately 20 days. What sample size is needed?
An advertising agency that serves a major radio station wants to estimate the mean amount of time that the station’s audience spends listening to the radio daily. From past studies, the standard deviation is estimated as 45 minutes.a. What sample size is needed if the agency wants to be
A consumer group wants to estimate the mean electric bill for the month of July for single family homes in a large city. Based on studies conducted in other cities, the standard deviation is assumed to be $60. The group wants to estimate the mean bill for July to within ±$15 with 99% confidence.a.
The inspection division of a state department which regulates trade measurement wants to estimate the mean amount of soft-drink fill in 2-litre bottles to within ±0.01 litres with 95%confidence. If it assumes that the standard deviation is 0.05 litres, what sample size is needed?
If a quality control manager wants to estimate the mean life of a new type of LED light globe to within 1,000 hours with 95%confidence and also assumes that the population standard deviation is 5,000 hours, what sample size is needed?
If the manager of a paint supply store wants to estimate the mean amount of paint in a 4-litre can to within ±0.015 litres with 95% confidence and also assumes that the standard deviation is 0.075 litres, what sample size is needed?
A survey is planned to determine the mean annual family medical expenses of employees of a large company which subsidises the health insurance of its staff. The management of the company wishes to be 95% confident that the sample mean is correct to within ±$50 of the population mean annual family
If you want to be 95% confident of estimating the population proportion to within a sampling error of ±0.02 and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?
If you want to be 99% confident of estimating the population proportion to within a sampling error of ±0.04, what sample size is needed?
If you want to be 99% confident of estimating the population mean to within a sampling error of ±20 and the standard deviation is assumed to be 100, what sample size is required?
If you want to be 95% confident of estimating the population mean to within a sampling error of ±5 and the standard deviation is assumed to be 15, what sample size is required?
Suppose that, in a survey of 600 employers, 126 indicate that they have used a recruitment service within the past two months to find new staff.a. Construct a 95% confidence interval for the population proportion of employers who have used a recruitment service within the past two months to find
The Australian Psychological Society conducted an online survey in 2016 of 1,000 adults and 518 adolescents. It found that 69% of adolescents reported consuming food from fast food restaurants at least once a week. (Psychology Week 2016, APS Compass for Life Wellbeing Survey accessed 5 July
The Australian Telecommunications Industry Ombudsman 2016 Annual Report states that 34.1% of new complaints in 2015–16 related to faults ( accessed 5 July 2017).Imagine that you take a survey of 1,000 Australian users and find that 36% of this sample report that they have had telecommunication
The number of older consumers in Australia is growing and they are becoming an important economic force. According to the Australian Bureau of Statistics, the proportion of the population aged 65 years and over increased from 14% in 2011 to 16% in 2016. (Australian Bureau of Statistics, Reflecting
A survey of 293 inhabitants of Tropical North Queensland in 2013 found that 45% considered increased property values were a negative impact of tourism in the region (Tropical North Queensland Social Indicators 2013 accessed 5 July 2017).a. Construct a 95% confidence interval for the proportion of
A survey of 500 highly educated women who left careers for family reasons found that 66% postponed their return to work due to difficulty in making suitable childcare arrangements.a. Construct a 95% confidence interval for the population proportion of highly educated women who have postponed their
A telco wants to estimate the proportion of mobile phone customers who would purchase a phone plan with unlimited standard calls and SMS and 2GB of data if it were made available at a substantially reduced cost. A random sample of 500 customers is selected. The results indicate that 190 of the
If n = 400 and X = 25, construct a 99% confidence interval estimate of the population proportion.
If n = 200 and X = 50, construct a 95% confidence interval estimate of the population proportion.
The data below represent the daily rate in Australian dollars for a double room or studio booking on the following Monday night at a sample of hotels, motels and motor lodges in 20 New Zealand cities and towns in July 2017. < MOTEL_2017 >
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
One of the major measures of the quality of service provided by any organisation is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpeting, has undergone a major expansion in the past several years. In
The data below represent the annual account fees for cheques made by a bank for a sample of 23 clients witha. Construct a 95% confidence interval for the population mean annual cheque fee.b. What assumption must you make about the population distribution in (a)?c. Interpret the interval constructed
The energy consumption of refrigerators sold in Australia and New Zealand is checked and appliances are given a star rating to guide consumers who are about to make purchases. The consumption in kilowatts per annum is also displayed for each model on the website . Suppose a consumer organisation
Water resources in many parts of Australia are being closely watched and restrictions or water-wise rules have been imposed on activities such as garden watering. Suppose that Sydney Water monitors water usage in a suburb and finds that for one summer the average household usage is 408 litres per
A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 20 greeting cards indicates a mean value of $4.95 and a standard deviation of $0.82.a. Assuming a normal distribution, construct a 95% confidence interval estimate of the
Construct a 95% confidence interval for the population mean, based on the numbers 1, 2, 3, 4, 5, 6 and 20. Change the number 20 to 7 and recalculate the confidence interval. Using these results, describe the effect of an outlier (i.e. extreme value) on the confidence interval.
Construct a 95% confidence interval estimate for the population mean, based on each of the following sets of data, assuming that the population is normally distributed:
If X– = 50, S = 15, n = 16, and assuming that the population is normally distributed, construct a 99% confidence interval estimate of the population mean μ.
If X– = 75, S = 24, n = 36, and assuming that the population is normally distributed, construct a 95% confidence interval estimate of the population mean μ.
Determine the critical value of t in each of the following circumstances:a. 1 - α = 0.95, n = 10b. 1 - α = 0.99, n = 10c. 1 - α = 0.95, n = 32d. 1 - α = 0.95, n = 65e. 1 - α = 0.90, n = 16
The inspection division of a state department that regulates trade measurement wants to estimate the actual amount of soft drink in 2-litre bottles at the local bottling plant of a large, nationally known soft-drink company. The bottling plant has informed the inspection division that the
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 3,000 hours. A random sample of 64 light globes indicates a sample mean life of 34,000 hours.a. Construct a
The manager of a paint supply store wants to estimate the actual amount of paint contained in 4-litre cans purchased from a nationally known manufacturer. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is equal to 0.08 litres. A random sample
Is it true in Example 8.1 that you do not know for sure whether the population mean is between 3,501.67 g and 3,712.33 g?Explain.
From the results of Example 8.1 regarding salmon farming, is it true that 95% of the sample means will fall between 3,501.67 g and 3,712.33 g? Explain.
Why is it not possible in Example 8.1 to have 100% confidence?Explain.
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