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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

10.104 Got Milk II Refer to Exercise 10.103. Wishing to demonstrate that the variability of fills is less for her model than for her competitor's, a sales representative for company A acquired a
10.105 Chemical Purity A chemical manufacturer claims that the purity of its product never varies by more than 2%. Five batches were tested and given purity readings of 98.2, 97.1, 98.9, 97.7, and
10.106 454-gram Cans? A cannery prints "weight 454 grams" on its label. The quality control supervisor selects nine cans at random and weighs them. He finds 445 and s 14.2. Do the data present
10.107 Reaction Time III A psychologist wishes to verify that a certain drug increases the reaction time to a given stimulus. The following reaction times (in tenths of a second) were recorded before
10.108 Food Production At a time when energy conservation is so important, some scientists think closer scrutiny should be given to the cost (in energy) of producing various forms of food. Suppose
10.109 Alcohol and Altitude The effect of alcohol consumption on the body appears to be much greater at high altitudes than at sea level. To test this theory, a scientist randomly selects 12 subjects
10.110 Stock Risks The closing prices of two common stocks were recorded for a period of 15 days. The means and variances area. Do these data present sufficient evidence to indi- cate a difference
10.111 Auto Design An experiment is conducted to compare two new automobile designs. Twenty people are randomly selected, and each person is asked to rate each design on a scale of 1 (poor) to 10
10.112 Safety Programs The data shown here were collected on lost-time accidents (the figures given are mean work-hours lost per month over a period of one year) before and after an industrial safety
10.113 Two Different Entrees To compare the demand for two different entrees, the manager of a cafeteria recorded the number of purchases of each entree on seven consecutive days. The data are shown
10.114 Pollution Control The U.S. Environmental Protection Agency limit on the allowable discharge of suspended solids into rivers and streams is 60 milligrams per litre (mg/L) per day. A study of
10.115 Enzymes Two methods were used to measure the specific activity (in units of enzyme activity per milligram of protein) of an enzyme. One unit of enzyme activity is the amount that catalyzes the
10.116 Connector Rods A producer of machine parts claimed that the diameters of the connector rods produced by its plant had a variance of at most 0.173 cm. A random sample of 15 connector rods from
10.117 Sleep and the University Student How much sleep do you get on a typical study night? A group of 10 university students were asked to report the number of hours that they slept on the previous
10.118 Arranging Objects The following data are the response times in seconds for n = 25 first graders to arrange three objects by size.Find a 95% confidence interval for the average re- sponse time
10.119 The NBA Finals Want to attend a pro-basketball finals game? The average prices for the NBA rematch of the Boston Celtics and the L.A. Lakers in 2010 compared to the average ticket prices in
10.120 Finger-Lickin' Good! Maybe too good, according to tests performed by the consumer testing division of Good Housekeeping. Nutritional informa- tion provided by KFC claims that each small bag of
10.121 Mall Rats One study investigated consumer habits at the mall. We tend to spend the most money shopping on the weekends, and, in particular, on Sundays from 4 to 6 P.M. Wednesday morning shop-
10.122 Border Wars As the costs of prescription drugs escalate, more and more American senior citizens are ordering prescriptions from Canada, or actually crossing the border to buy prescription
1. American martens feed on a variety of small mammals, birds, insects, fish, carrion, and vegetation. Marten food habits differ substantially in different geographic areas. Do the data indicate that
2. Peanut butter is one of the favourite foods of North Americans. Do American martens have a taste for peanut butter as well? Answer by comparing the effect of peanut butter and the control.The
3. Construct a 95% confidence interval to estimate the average difference in days taken for the marten to visit a chicken track box and a peanut butter track box. What do you conclude about the
4. Based on your answers to parts 1, 2, and 3, what can you conclude about the order of the effectiveness of the four different baits?The American marten has become a focal species for the
a. It is of interest to know if the sample data suggest the average blood glucose level is higher than 7.0 mmol/L. (i) State the appropriate hypotheses. (ii) Compute the test statistic for the
b. A diabetes researcher would like to study the variability in the fasting blood glu- cose level readings for the selected person in parta. The researcher believes that fasting blood glucose never
c. At a diabetic clinic, a group of people considered to have prediabetes (impaired fasting glucose) were randomly selected. Then they were randomly assigned in two groups, namely treatment group
d. The researcher was not too sure about the assumption of equality of variances and was under the impression that the population variance of the placebo group is greater than the variance of the
e. Ten adults with symptoms of diabetes were randomly selected and a random blood glucose test was administered before and after a medication. Their blood glucose level readings were gathered before
You wish to show that the average hourly wage of clerical workers in the province of New Brunswick is different from $14, which is the national average. This is the alterna- tive hypothesis, written
A milling process currently produces an average of 3% defectives. You are interested in showing that a simple adjustment on a machine will decrease p, the proportion of defectives produced in the
According to Statistics Canada the mean birth weight of newborn babies in Canada is 3.372 kg for both sexes. However, a pediatrician in Alberta believes that mean birth of newborn babies for both
Based on the online survey of a representative national sample of 1,006 Canadian adults, 54% respondents believe Canada should be a melting pot. A researcher thinks that the melting pot is
For the test of hypothesis in Example 9.1, the average hourly wage x for a random sample of 100 New Brunswick clerical workers might provide a good test statistic for testing Ho: 14 versus H: 14 If
The average weekly earnings for women in managerial and professional positions is $670. Do men in the same positions have average weekly earnings that are higher than those for women? A random sample
The daily yield for a local chemical plant has averaged 880 metric tons for the last several years. The quality control manager would like to know whether this average has changed in recent months.
Refer to Example 9.7. The quality control manager wants to know whether the daily yield at a local chemical plant-which has averaged 880 metric tons for the last several years has changed in recent
Standards set by government agencies indicate that Canadians should not exceed an average daily sodium intake of 3300 milligrams (mg). To find out whether Canadians are exceeding this limit, a sample
Refer to Example 9.7. Calculate and the power of the test (1-3) when u is actually equal to 870 metric tons.
9.1 Find the appropriate rejection regions for the large-sample test statistic z in these cases:a. A right-tailed test with a = 0.01b. A two-tailed test at the 5% significance level
9.2 Refer to Exercise 9.1. Suppose that the observed value of the test statistic was z = 2.16. For the rejection regions constructed in parts a and b of Exercise 9.1, draw the appropriate conclusion
9.5 For the three tests given in Exercise 9.4, use the p-value to determine the significance of the results. Explain what "statistically significant" means in terms of rejecting or accepting Ho and H.
9.7 Refer to Exercise 9.6.a. Calculate the p-value for the test statistic in partd. b. Use the p-value to draw a conclusion at the 5% significance level.c. Compare the conclusion in part b with the
9.8 Refer to Exercise 9.6. You want to test Ho 2.3 against H: > 2.3.a. Find the critical value of x used for rejecting Ho.b. Calculate B = P(accept Ho when = 2.4).c. Repeat the calculation of for =
9.10 Airline Occupancy Rates High airline occupancy rates on scheduled flights are essential to corporate profitability. Suppose a scheduled flight must average at least 60% occupancy in order to be
9.11 Ground Beef The meat department of a local supermarket chain packages ground beef in trays of two sizes. The smaller tray is intended to hold 1 kilo- gram (kg) of meat. A random sample of 35
9.12 Invasive Species In a study of the pernicious giant hogweed, Jan Pergl and associates compared the density of these plants in two different sites within the Caucasus region of Russia. In its
9.13 Advertising at the Movies "Welcome to the new movie pre-show!" Before you can see the newly released movie you have just paid to see, you must sit through a variety of trivia slides, snack bar
9.14 Potency of an Antibiotic A drug manufac- turer claimed that the mean potency of one of its antibi- otics was 80%. A random sample of n = 100 capsules were tested and produced a sample mean of
9.15 Flextime Many companies are becoming involved in flextime, in which a worker schedules his or her own work hours or compresses work weeks. A com- pany that was contemplating the installation of
9.16 Raise Your MCAT Test Scores! There are many books and crash courses available to prepare for the MCAT examination. An organization that offers such courses claims the average score improvement
9.17 What's Normal? What is normal, when it comes to people's body temperatures? A random sam- ple of 130 human body temperatures, provided by Allen Shoemaker in the Journal of Statistical Education,
9.18 Sports and Achilles Tendon Injuries Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and
To determine whether car ownership affects a student's academic achievement, two random samples of 100 male students were each drawn from the student body. The grade point average for the n = 100
Construct a 95% confidence interval for the difference in average academic achieve- ments between car owners and non-owners. Using the confidence interval, can you con- clude that there is a
9.19 Independent random samples of 80 measure- ments were drawn from two quantitative populations, 1 and 2. Here is a summary of the sample data: a. If your research objective is to show that , is
9.21 Suppose you wish to detect a difference between and (either or ) and, instead of running a two-tailed test using a = 0.05, you use the following test procedure. You wait until you have collected
9.22 Cure for the Common Cold? An experi- ment was planned to compare the mean time (in days) required to recover from a common cold for per- sons given a daily dose of 4 mg of vitamin C versus those
9.23 Healthy Eating Canadians are becoming more conscious about the importance of good nutrition, and some researchers believe we may be altering our diets to include less red meat and more fruits
9.24 Lead Levels in Drinking Water Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following means and standard deviations of lead levels (in
9.25 Starting Salaries, again In an attempt to compare the starting salaries for university graduates who majored in education and the social sciences (see Exercise 8.52), random samples of 50 recent
9.26 Hotel Costs In Exercise 8.19, we explored the average cost of lodging at three different hotel chains. We randomly select 50 billing statements from the computer databases of the Marriott,
9.27 Hotel Costs || Refer to Exercise 9.26. The table below shows the sample data collected to compare the average room rates at the Westin and Doubletree hotel chains." a. Do the data provide
9.28 MMT in Gasoline The addition of MMT, a compound containing manganese (Mn), to gasoline as an octane enhancer has caused concern about human exposure to Mn because high intakes have been linked
9.29 Noise and Stress In Exercise 8.55, you compared the effect of stress in the form of noise on the ability to perform a simple task. Seventy subjects were divided into two groups; the first group
9.30 What's Normal II Of the 130 people in Exer- cise 9.17, 65 were female and 65 were male." The means and standard deviations of their temperatures are shown below.a. Use the p-value approach to
Regardless of age, about 20% of Canadian adults participate in fitness activities at least twice a week. However, these fitness activities change as the people get older, and occasionally
9.31 A random sample of n = 1000 observations from a binomial population produced x = 279.a. If your research hypothesis is that p is less than 0.3, what should you choose for your alternative
9.34 R and M Entertainment On behalf of the Canadian Teachers Federation (CTF), Erin Research conducted a study on Canadian children and their experience with communication media. The research
9.35 Plant Genetics A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring result- ing from this cross will have red
9.36 Early Detection of Breast Cancer Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Sup- pose a community public health department
9.37 Sweet Potato Whitefly Suppose that 10% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected, and 25 are
9.38 Taste Testing In a head-to-head taste test of store-brand foods versus national brands, Consumer Reports found that it was hard to find a taste difference in the two.12 If the national brand is
9.39 Avian Flu Avian flu is clearly on the radar of Canadians. Given the amount of media coverage on the Avian Flu issue, it is not surprising to find that about 60% are concerned about it. However,
9.40 A Cure for Insomnia An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 80% of people suffering from insom- nia. After examining the dosage, we feel that
9.41 Avian Flu, continued Refer to Exercise 9.39. The research report further indicates evidence that the public is somewhat concerned about whether or not Canadian health authorities are prepared to
9.42 Aboriginal People in Canada According to the most recent census data, Aboriginal people account for approximately 3.3% of the Canadian population. 14 However, the female-to-male ratio is
9.43 Love for Pets in Canada Canadians own a total of 8 million dogs and cats. This total breaks down to approximately 3.5 million dogs and 4.5 million cats in the country, according to Statistics
The records of a hospital show that 52 men in a sample of 1000 men versus 23 women in a sample of 1000 women were admitted because of heart disease. Do these data pres- ent sufficient evidence to
9.45 Refer to Exercise 9.43. Suppose, for practical reasons, you know that p, cannot be larger than p.a. Given this knowledge, what should you choose as the alternative hypothesis for your
9.47 Treatment versus Control An experiment was conducted to test the effect of a new drug on a viral infection. The infection was induced in 100 mice, and the mice were randomly split into two
9.48 Tai Chi and Fibromyalgia A new study (Exercise 7.13) indicates that tai chi, an ancient Chi- nese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The
9.49 Movie Marketing Marketing to targeted age groups has become a standard method of advertising, even in movie theatre advertising. Advertisers use com- puter software to track the demographics of
9.50 M&Ms In Exercise 8.60, you investigated whether Mars, Inc., uses the same proportion of red M&Ms in its plain and peanut varieties. Random sam- ples of plain and peanut M&Ms provide
9.51 Hormone Therapy and Alzheimer's Disease In the last few years, many research stud- ies have shown that the purported benefits of hormone replacement therapy (HRT) do not exist, and in fact, that
9.52 HRT, continued Refer to Exercise 9.51. Calculate a 99% lower one-sided confidence bound for the difference in the risk of dementia for women using hormone replacement therapy versus those who do
9.53 Clopidogrel and Aspirin A large study was con- ducted to test the effectiveness of clopidogrel in combina- tion with aspirin in warding off heart attacks and strokes. 19 The trial involved more
9.54a. Define a and for a statistical test of hypothesis.b. For a fixed sample size n, if the value of a is decreased, what is the effect on ?c. In order to decrease both a and for a particular
9.55 What is the p-value for a test of hypothesis? How is it calculated for a large-sample test?
9.56 What conditions must be met so that the z test can be used to test a hypothesis concerning a population mean?
9.57 Define the power of a statistical test. As the alternative value of gets farther from , how is the power affected?
9.58 Acidity in Rainfall Refer to Exercise 8.34 and the collection of water samples to estimate the mean acidity (in pH) of rainfalls in Eastern Canada. As noted, the pH for pure rain falling through
9.59 Washing Machine Colours A manufacturer of automatic washers provides a particular model in one of three colours. Of the first 1000 washers sold, it is noted that 400 were of the first colour.
9.60 Commercials in Space The commercialism of our space program20 was the topic of Exercise 8.67. In a survey of 500 men and 500 women, 20% of the men and 26% of the women responded that space
9.61 Bass Fishing The pH factor is a measure of the acidity or alkalinity of water. A reading of 7.0 is neutral; values in excess of 7.0 indicate alkalinity; those below 7.0 imply acidity. Loren Hill
9.62 Traffic Tickets An Ontario website (www.trafficticket.com) claims "We fully dismiss [at least] 94% of all cases."a. Suppose that we examine 25 cases and exactly 15 were fully dismissed. Would
9.63 White-Tailed Deer In an article entitled "A Strategy for Big Bucks," Charles Dickey discusses studies of the habits of white-tailed deer that indicate that they live and feed within very limited
9.64 Female Models In a study to assess various effects of using a female model in automobile adver- tising, 100 men were shown photographs of two auto- mobiles matched for price, colour, and size,
9.65 Bolts Random samples of 200 bolts manufac- tured by a type A machine and 200 bolts manufactured by a type B machine showed 16 and 8 defective bolts, respectively. Do these data present
9.66 Biomass Exercise 7.74 reported that the bio- mass for tropical woodlands, thought to be about 35 kilograms per square metre (kg/m), may in fact be too high and that tropical biomass values vary
9.67 Anti-Terrorism Bill C-36 The Anti-Terrorism Bill was passed by the House of Commons on November 28, 2001. Many people argued that the law increased burden for charities. A researcher believed

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