Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 7, Problem 7.65CE
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The superior product out of soft drink
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Studies have shown that omega-3 fatty acids have a wide variety of health benefits. Omega-3 oils can be found in foods such as fish, walnuts, and flaxseed. A company selling milled flaxseed advertises that one tablespoon of the product contains, on average, at least 3800 mg of ALNA, the primary omega-3.
a) The company plans to conduct a test to ensure that there is sufficient evidence that its claimiscorrect. Tobesafe,thecompanywantstomakesurethatevidenceshowsthe average is higher than 3800 mg. What are the null and alternative hypotheses?
b) Suppose, instead, that a consumer organization plans to conduct a test to see if there is evidence against the claim that the product contains an average of 3800 mg per tablespoon. The consumer organization will only take action if it finds evidence that the claim made by the company is false and that the actual average amount of omega-3 is less than 3800 mg. What are the null and alternative hypotheses?
In a winter of an epidemic flu, the parents of 2000 babies were surveyed by researchers at a well-known pharmaceutical company to determine if the company’s new medicine was effective after two days. Among 120 babies who had the flu and were given the medicine, 29 were cured within two days. Among 280 babies who had the flu but were not given the medicine, 56 recovered within two days. Is there any significant indication that supports the company’s claim of the effectiveness of the medicine? Use a significance level of 0.10
A. What type of Hypothesis Testing should be used?
B. What are the null and alternative hypothesis?
C. What are the significance level and type of test?
D. What is the critical value?
E. What is the standardized test statistic?
F. What is the Statistical Decision?
In a winter of an epidemic flu, the parents of 2000 babies were surveyed by researchers at a well-known pharmaceutical company to determine if the company’s new medicine was effective after two days. Among 120 babies who had the flu and were given the medicine, 29 were cured within two days. Among 280 babies who had the flu but were not given the medicine, 56 recovered within two days. Is there any significant indication that supports the company’s claim of the effectiveness of the medicine? Use a significance level of 0.10
Chapter 7 Solutions
Introduction to Business Statistics
Ch. 7.1 - What is the difference between a continuous...Ch. 7.1 - What is a probability density function and how is...Ch. 7.1 - Why is the total area beneath a probability...Ch. 7.1 - Prob. 7.4ECh. 7.2 - It has been stated that the nomal distribution is...Ch. 7.2 - Prob. 7.6ECh. 7.2 - Prob. 7.7ECh. 7.2 - Prob. 7.8ECh. 7.2 - Prob. 7.9ECh. 7.2 - The Canada Urban Transit Association has reported...
Ch. 7.2 - Prob. 7.11ECh. 7.2 - In 2009, the average charge for tax preparation by...Ch. 7.2 - It has been reported that the average hotel...Ch. 7.2 - The average American family of four spends $5000...Ch. 7.2 - Prob. 7.15ECh. 7.3 - The normal distribution is really a family of...Ch. 7.3 - In the standard normal distribution, approximately...Ch. 7.3 - A Continuous random variable, x, is normally...Ch. 7.3 - Prob. 7.19ECh. 7.3 - Prob. 7.20ECh. 7.3 - Prob. 7.21ECh. 7.3 - Prob. 7.22ECh. 7.3 - Prob. 7.23ECh. 7.3 - Prob. 7.24ECh. 7.3 - Prob. 7.25ECh. 7.3 - Prob. 7.26ECh. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - Prob. 7.28ECh. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - Prob. 7.32ECh. 7.3 - It has been reported that households in the West...Ch. 7.3 - Andre is a fearless circus performer who gets shot...Ch. 7.3 - Drying times for newly painted microwave oven...Ch. 7.3 - KleerCo supplies an under-hood, emissionscontrol...Ch. 7.3 - Prob. 7.37ECh. 7.3 - Prob. 7.38ECh. 7.4 - What is the correction for continuity and why is...Ch. 7.4 - Under what circumstances is it permissible to use...Ch. 7.4 - In a certain binomial distribution, =0.25 and n=40...Ch. 7.4 - In a certain binomial distribution, =0.30 and n=20...Ch. 7.4 - Prob. 7.43ECh. 7.4 - Prob. 7.44ECh. 7.4 - Prob. 7.45ECh. 7.4 - Prob. 7.46ECh. 7.4 - Prob. 7.47ECh. 7.4 - Repeat Exercise 7.46, but without using the...Ch. 7.5 - What is the relationship between the Poisson...Ch. 7.5 - Every day, drivers arrive at a tollbooth. If the...Ch. 7.5 - The main switchboard at the Home Shopping Network...Ch. 7.5 - A random variable is Poision distributed with =1.5...Ch. 7.5 - A random variable is Poision distributed with...Ch. 7.5 - A random variable is Poision distributed with...Ch. 7.5 - The owner of a self-service carwash has found that...Ch. 7.5 - A taxi dispatcher has found that successive calls...Ch. 7.5 - During 2008, U.S. general aviation pilots had 1.20...Ch. 7.5 - The Bureau of Labor Statistics reports the...Ch. 7.6 - A computer statistical package has simulated 1000...Ch. 7.6 - Prob. 7.60ECh. 7.6 - Prob. 7.61ECh. 7.6 - Prob. 7.62ECh. 7 - According to a recent survey, 35% of the adult...Ch. 7 - Prob. 7.64CECh. 7 - Prob. 7.65CECh. 7 - During an annual heating season, the average gas...Ch. 7 - It has been reported that the average monthly cell...Ch. 7 - During 2004, the average number of flying hours...Ch. 7 - During fiscal 2008, the average daily volume for...Ch. 7 - For itemized tax returns in the $60,000—$75,000...Ch. 7 - Of the 1.0 million persons of voting age in Maine,...Ch. 7 - A public relations agency tells its client that...Ch. 7 - Given the results of Exercise 7.72, evaluate the...Ch. 7 - A researcher is studying a particular process and...Ch. 7 - A safety researcher has found that fourth to sixth...Ch. 7 - The number of defects in rolls of aluminum sheet...Ch. 7 - The mileage death rate for motorcycle riders has...Ch. 7 - The “20-ounce” package of mozzarella cheese...Ch. 7 - State Police Academy graduates from a large gradua...Ch. 7 - The trainer for a professional football team has...Ch. 7 - The precooked weight of hamburgers at a gourmet...Ch. 7 - Boxes are filled with sugar by a machine that is...Ch. 7 - In Exercise 7.82, the company would like to put in...Ch. 7 - Discount Micros, a computer mail-order company,...Ch. 7 - The U-Drive car rental corporation has found that...Ch. 7 - Ronnie Rogers, the customer relations manager for...Ch. 7 - A storage warehouse in a relatively remote part of...
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- A local bookseller carefully collectsdata on the customers that enter her store. She uses the term“unit” to describe either a customer that comes in alone ora group of customers that come in together. Based on pastexperience, she estimates that 8% of the units who enter herstore will make some type of purchase. It appears that theunits are independent.In one hour, ten units enter her store. What is theprobability that at least one of them makes a purchase?A) 0.038 B) 0.378 C) 0.434D) 0.566 E) 0.812arrow_forwardSuppose researchers do an epidemiologic investigation of people entering a sexually transmitted disease clinic. They find that 160 of 200 patients who are diagnosed as having gonorrhea and 50 of 105 patients who are diagnosed as having nongonococcal urethritis have had previous episodes of urethritis. 8.1 Are the present diagnosis and prior episodes of urethritis associated?arrow_forwardA study was conducted using undergraduates at a urban university who volunteered to participate in the research as partial fulfillment of a course requirement. One of the items studied was the amount of alcohol consumed (in drinks) in any one day for the past month. Administrators hypothesize that freshmen consume more alcohol than juniors. Based on the information in the table below, what can be concluded with an a of 0.107 freshmen juniors ân = 6.6 i2 = 7.6 ô1 = 1.2 ôz = 2.2 ni- 15 n2 = 14 a) What is the appropriate test statistic? --Select--- b) Condition 1: ---Select-- Condition 2: ---Select--- c) Obtain/compute the appropriate values to make a decision about Ho. ; Test Statistic = Critical Value = Decision: --Select--- d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below. e) Compute the corresponding effect size(s) and indicate magnitude(s). If not appropriate, input and/or select "na" below. d= ; Magnitude: ---Select--- ; Magnitude: --Select-arrow_forward
- Researchers want to test whether an Indian child's school grades are influenced by his or her caste. They believe graders simply take 10 points off the score of a test written by a student belonging to a lower caste. In order to test this hypothesis, they obtain the scores of children of higher and lower castes, on a test on which children are generally believed to do equally well. In their sample, among the 45 children belonging to the higher castes, the average grade was 74, with a standard deviation of 12. Among the 41 children belonging to the lower castes, the average grade was 61, with a standard deviation of 11. (a) Test the hypothesis that the difference in the mean scores of children of higher castes and the children of lower castes is 10 points at 1% significance level. (b) Define a two-sided confidence interval for the difference in the means. (c) Assuming that the caste bias does not impact the variance of the grades, rerun your hypothesis. (d) Report your two-sided…arrow_forwardTo test the effect of a new exercise routine on muscle growth, a researcher sets up the following experiment: 60 volunteers subjects (40 men and 20 women) of average build are selected to participate in the study. Their body mass and muscle sizes (biceps, thighs, etc.) are measured. The researcher gives all the men a DVD with the new exercise routine, and the women a DVD with a standard routine, but only the researcher knows this.The results of the experiment are likely to be invalid mostly because the subjects were volunteers. the treatment group and control group were not the same size. the gender of the patient is a confounding variable in this experiment. the subjects did not know if they were getting the real treatment. None of the abovearrow_forwardIn a winter with a flu epidemic, a well-known pharmaceutical company studied 2,000 babies to determine if the company's new drug was effective after two days. Among 120 babies who had the flu and were given the drug, 29 were cured within two days. Among 280 babies who had the flu but were not given the drug, 56 were cured within two days. Is there any significant indication to support the company's claim of the drug's effectiveness? Note:The exercise in the image is the original, it is in Spanish, but it is easy to understand.arrow_forward
- a) Are gender and age of contracting the disease independent of one another (α ≤ .05)? b) A researcher believes that people in the 41-55 age group are three times as likely to develop the disease as are those in each of the two younger age groups, while those in the 56 + age group are only twice as likely (relative to those in the two youngest groups). The two youngest age groups are not expected to differ from each other. Do the data support these beliefs (α ≤ .01)? c) It is also believed that, relative to males, the proportion of females in the 56 + age group that develops the disease is significantly different from the proportion of females in the 10-25 age group that develops the disease. Test this belief with α ≤ .05. Answers: 1. a) χ2 = 4.112, do not reject H0: gender and age of contracting the disease are independent; b) χ2 = 14.03, reject H0: the data do not support the researcher's beliefs; c) χ2 = 2.068, do not reject H0: it appears that this belief is not…arrow_forwardTo test the effect of a new exercise routine on muscle growth, a researcher sets up the following experiment: 60 volunteers subjects (40 men and 20 women) of average build are selected to participate in the study. Their body mass and muscle sizes (biceps, thighs, etc.) are measured. The researcher gives all the men a DVD with the new exercise routine, and the women a DVD with a standard routine, but only the researcher knows this. The results of the experiment are likely to be invalid mostly because:• the subjects were volunteers.• the gender of the volunteer is a confounding variable in this experiment.• the subjects did not know if they were getting the real treatment.• none of the above. It would improve the experiment if the researchers:• gave the new workout to the women.• gave everyone the same work out.• did not use so many women.• used the same number of men and women and gender-non-conforming subjectsarrow_forwardA random sample of 1200 apples was taken from a large consignment and found that 10% of them are bad. The supplier claims that only 2% are bad. Test his claim.arrow_forward
- 9t,12. Can vaccination be regarded as preventive measure for smallpox, from the data given below? "Of 1,482 persons in a locality exposed to smallpox, 368 in all were attacked. "Of 1,482 persons, 343 had been vaccinated and of these only 35 were attacked.'arrow_forwardIn a Japanese study, “researchers looked at 35 peoplewith lower back pain who were enrolled in an aquatic exercise program, which included swimming and walk-ing in a pool. Almost all of the patients showed improve-ments after six months, but the researchers found that those who participated at least twice weekly showedmore significant improvement that those who wentonly once per week.”Which of the following statements is true?a) This experiment proves that swimming causes areduction in lower back pain.b) This study is a poorly designed experiment sincethere is no control group and no randomization.c) Conclusions based on this observational study aresuspect since participation in the aquatic programmay be confounded with other lifestyle behaviors thatmay cause the improvement in lower back health.d) Conclusions based on this observational study aresuspect since a sample size of 35 is too small.e) This study is not an observational study since theaquatic program is a treatment.arrow_forwardTo test the effect of a new exercise routine on muscle growth, a researcher sets up the following experiment: 60 volunteers subjects (40 men and 20 women) of average build are selected to participate in the study. Their body mass and muscle sizes (biceps, thighs, etc.) are measured. The researcher gives all the men a DVD with the new exercise routine, and the women a DVD with a standard routine, but only the researcher knows this. The results of this experiment are likely to be invalid mostly becausearrow_forward
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