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business
statistics for business and economics
Questions and Answers of
Statistics For Business And Economics
Stability of compounds in new drugs. Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise
(p. 77). Recall that two important values computed from the testing phase are the fraction of compound unbound to plasma (fup) and the fraction of compound unbound to microsomes (fumic). A key
Facial structure of CEOs. Refer to the Psychological Science (Vol. 22, 2011) study on using a chief executive officer’s facial structure to predict a firm’s financial performance, Exercise
(p. 339). Recall that the facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500 firms was determined. The sample resulted in x =
and s = .15. An analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of m = 2.2. Do you
Ride-hailing service. A research article published in the Academy of Entrepreneurship Journal (Vol. 27, 2021) evaluates the service quality of a ride-hailing service in Bangkok, where the reliability
with a standard deviation 0.73.
Trading skills of institutional investors. The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on
Producer’s and consumer’s risk. In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing
Unethical corporate conduct. Refer to the Behavioral Research in Accounting (July 2015) study of unethical corporate conduct, Exercise
(p. 338). Recall that each in a sample of 86 accounting graduate students was asked to perform an unethical task (e.g., to bribe a customer), and each subject’s intention to comply with the
(intention to comply with the unethical request)]. Summary statistics on the 86 scores follow: x = 2.42, s = 2.84. One researcher, of the opinion that subjects will tend to perform the unethical
Time required to complete a task. When a person is asked, “How much time will you require to complete this task?” cognitive theory posits that people (e.g., a business consultant) will typically
Time spent in fitness center. The owner of a fitness center wants to compare the time his customers spend on each visit to his center during working hours and the time they spend on each visit
20.65 Outside working hours 150
6.02a. Determine if the customers spent less than 2 hours per visit during working hours at a 5% significance level.b. Determine if the customers spent more than
hours per visit outside of working hours at a 5% significance level.
Wage distribution. Refer to the wage distribution in Malaysia published in the Journal of Physics in 2020, Exercise
(p. 339). Data were collected by means of a survey from 13,089 workers, 9,493 of which are from urban regions. The workers from urban regions reported an average wage of RM2,725.83 with a standard
Length of stay. According to the data reported by the Tourism Bureau, Ministry of Transportation and Communications in CEIC, the average length of stay in Taiwan from January 2008 to February 2021
Buy-side vs. sell-side analysts’ earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) study of earnings forecasts of buy-side and sell-side analysts, Exercise
(p. 105). Recall that data were collected on 3,526 forecasts made by buy-side analysts and 58,562 forecasts made by sell-side analysts, and the relative absolute forecast error was determined for
-0.05 Standard Deviation
0.85 Source: Based on B. Groysberg, P. Healy, and C. Chapman, “Buy-Side vs. Sell-Side Analysts’ Earnings Forecast,” Financial Analysts Journal, Vol. 64, No. 4, July/August 2008.a. Conduct a
Solder-joint inspections. Current technology uses highresolution X-rays and lasers for inspection of solderjoint defects on printed circuit boards (PCBs) (Tempo Automation, August 2019) A
Managers who engage in “coopetition.” In business, firms that both cooperate and compete with other firms are described as engaging in “coopetition.” A study published in Industrial
and the sample standard deviation was s = 3.04.a. Conduct a test (using a = .05) to determine if the true mean external tension level of all managers who engage in coopetition differs from
points.b. Find a 95% confidence interval for the true mean external tension level of all managers who engage in coopetition.c. Explain how the confidence interval of part b can be used to infer
Support for an entrepreneur’s project. Refer to the Academy of Management Journal (December 2019) study of crowdfunding backers for an entrepreneur’s project, Exercise
(p. 337). Recall that the researchers collected BACKERS data on the number of crowdfunding backers for each in a sample of 1,460 entrepreneurial projects pitched on the internet via video. The data
For each of the following rejection regions, sketch the sampling distribution of t and indicate the location of the rejection region on your sketch:a. t 7
where df = 11b. t 6 -1.533 where df = 4c. t 6 -1.703 or t 7
where df = 27d. For each of the parts a toc, what is the probability that a Type I error will be made?
A random sample of n observations is selected from a normal population to test the null hypothesis that m = 38. Specify the rejection region for each of the following combinations of Ha,a, and n:a.
Suppose you are testing a hypothesis for a sample of 25 people for the null hypothesis H0: m … 85 versus the alternative hypothesis Ha: m 7 85. The population standard deviation is unknown and the
Fresh full cream fresh milk. Refer to the data concerning customers’ satisfaction with the fresh full cream milk available in Australia in 2020, Exercise
(p. 346). The accompanying table shows the best milk brands in Australia, as rated by consumers in Canstar Blue’s 2020 review. Suppose consumers believe that the true mean price of the milk was
Farmers’ Own
ALDI Farmdale
a2 Milk
Coles
Devondale
Dairy Farmers 4 Pauls 6 Woolworths
Pura
a. Set up the null and alternative hypotheses for testing the consumers’ belief.b. Compute the test statistic.c. Given the rejection region for the test.d. Make the appropriate conclusion using a =
Accidents at construction sites. In a study published in the Business & Economics Research Journal (April 2015), occupational accidents at three construction sites in Turkey were monitored. The total
Supermarket product line unit price. Refer to the unit prices (in Kyat) of eight electronic accessories in a supermarket located in Mandalay, Exercise
(p. 375). The prices are listed in the following table. The data provides x =
and s = 33.80. Let m represent the average unit price of all the electronic accessories products in the supermarket. Suppose you want to determine if the true value m differs from 60 Kyat.
93.96
57.49
13.22
14.96a. Specify the null and alternative hypotheses for this test.b. Since x =
is less than 60, the supermarket owner wants to reject the null hypothesis. What are the problems with using such a decision rule?c. Compute the value of the test statistic.d. Find the approximate
(p. 346) you found a 95% confidence interval for m. Does this interval support your conclusion in part f?
Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in Egyptian tombs, Exercise
(p. 376). The radon levels—measured in becquerels per cubic meter (Bq>m3 )—in the inner chambers of a sample of 12 tombs are listed in the table shown below. For the safety of the guards and
Performance of stock screeners. Recall, from Exercise
(p. 376), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment
-.1 -1.6
a. State H0 and Ha for this test.b. Locate the values of x and s on the printout, and then use these values to compute the test statistic. Verify that your calculation is correct by comparing it with
Oxygen bubble velocity in a purification process. Refer to the Chemical Engineering Research and Design (March 2013) study of a method of purifying nuclear fuel waste, Exercise
(p. 347). Recall that the process involves oxidation in molten salt and tends to produce oxygen bubbles with a rising velocity. To monitor the process, the researchers collected data on bubble
* 10-6 , the researchers discovered that the true mean bubble rising velocity is m = .338.a. Conduct a test of hypothesis to determine if the true mean bubble rising velocity for the population from
* 10-6 ? Explain.
0.261
0.266
0.312
0.317
0.251
0.339
0.178
0.307
0.319
0.169
0.270
0.228
7.58 Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of grocery store shoppers’ judgments, Exercise
(p. 105). For one part of the study, 11 consumers were told to put their arm in a flex position (similar to carrying a shopping basket) and then each consumer was offered several choices between a
China’s ranking in government accountability. Refer to the tradingeconomics.com February 2020 assessment of China’s ranking in government accountability, Exercise
(p. 348). Recall that each in a small sample of 12 sources provided a ranking for China, where a rank of 0 is the lowest rank possible and a rank of 100 is the highest rank possible. An analysis of
and s = 5.71. A Chinese government official has assured China’s residents that the population mean rank of China is at least 15. Do you agree? Test using a = .05.
Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise
(p. 348). Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and that the amount of dioxide (milligrams/liter)—a measure of
Yes
No Source: Based on A. Permanyer et al., “Crude Oil Biodegradation and Environmental Factors at the Riutort Oil Shale Mine, SE Pyrenees,” Journal of Petroleum Geology, Vol. 33, No. 2, April 2010
Traffic. Refer to the survey conducted on the traffic counts and accidents that occurred in Bloomington during 2019, Exercise
(p. 337). The data set lists the road names starting with the letters A or B, states whether the traffic collision was a case of hit and run (Yes or No), and notes the highest number of vehicles
Unequal weights. Jim and Maya purchased two packs of cookies each from a store. Suppose each pack weighs 50 grams according to the label on the packaging. Jim and Maya weighed each pack and recorded
Suppose a random sample of 100 observations from a binomial population gives a value of pn = .63 and you wish to test the null hypothesis that the population parameter p is equal to .70 against the
Suppose the sample in Exercise
has produced pn = .83 and we wish to test H0: p = .9 against the alternative Ha: p 6 .9.a. Calculate the value of the z-statistic for this test.b. Note that the numerator of the z-statistic (pn - p0
(p. 354), in which 50 consumers tastetested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below.a. Test H0: p = .5 against Ha: p 7 .5, where p
For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section
Use the applet Hypotheses Test for a Proportion to investigate the relationships between the probabilities of Type I and Type II errors occurring at levels .05 and .01. For this exercise, use n =
● Large-Sample Test of Hypothesis About a Population Proportion 425 and at the .01 level as the applet is run more and more times? What type of error has occurred when the null hypothesis is
Use the applet Hypotheses Test for a Proportion to investigate the effect of the true population proportion p on the probability of a Type I error occurring. For this exercise, use n = 100, and
Teacher job satisfaction. An article published in the Educational Review (2020) investigated the relationship between teacher job satisfaction, working conditions at the school, and teacher
Water consumption. Refer to the data on the amount of water consumed by each household in Portland, Exercise
(p. 354). Recall the sample of 250 households in Portland, 100 of which reported that they use 20 gallons of water per day for showering. Also recall the claim that p, the true proportion of the
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