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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

8.72 Find a 99% lower confidence bound for the binomial proportion p when a random sample of n=400 trials produced x = 196 successes.
8.74 Suppose you wish to estimate a population mean based on a random sample of n observations, and prior experience suggests that or 12.7. If you wish to estimate correct to within 1.6, with
8.75 Suppose you wish to estimate a binomial parameter p correct to within 0.04, with probability equal to 0.95. If you suspect that p is equal to some value between 0.1 and 0.3 and you want to be
8.76 Independent random samples of n = n = n observations are to be selected from each of two populations 1 and 2. If you wish to estimate the difference between the two population means correct to
8.77 Independent random samples of n = n = n observations are to be selected from each of two bino- mial populations 1 and 2. If you wish to estimate the difference in the two population proportions
8.78 Operating Expenses A random sampling of a company's monthly operating expenses for n = 36 months produced a sample mean of $5474 and a standard deviation of $764. Find a 90% upper confidence
8.79 Fear Factor II Exercise 8.21 discussed a research poll done by EKOS Research to determine whether Canadians think the world is more dangerous today than 25 years ago. Suppose you were designing
8.80 Political Corruption A questionnaire is designed to investigate attitudes about political corruption in government. The experimenter would like to survey two different groups-Liberals and
8.81 Less Red Meat! Canadians are becoming more conscious of the importance of good nutrition, and some researchers believe that we may be altering our diets to include less red meat and more fruits
8.82 Red Meat, continued Refer to Exercise 8.81. The researcher selects two groups of 400 subjects each and collects the following sample information on the annual beef consumption now and 10 years
8.83 Hunting Season If a wildlife service wishes to estimate the mean number of days of hunting per hunter for all hunters licensed in the province during a given season, with a bound on the error of
8.84 Polluted Rain Suppose you wish to estimate the mean pH of rainfalls in an area that suffers heavy pollution due to the discharge of smoke from a power plant. You know that or is in the
8.85 pH in Rainfall Refer to Exercise 8.84. Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area along
8.86 GPAs You want to estimate the difference in grade point averages between two groups of univer- sity students accurate to within 0.2 grade point, with probability approximately equal to 0.95. If
8.87 Selenium, again Refer to the comparison of the daily adult intake of selenium in two different regions of Canada in Exercise 8.48. Suppose you wish to estimate the difference in the mean daily
8.88 State the Central Limit Theorem. Of what value is the Central Limit Theorem in large-sample statistical estimation?
8.90 Independent random samples of n = 50 and n = 60 observations were selected from populations 1 and 2, respectively. The sample sizes and computed sample statistics are given in the table: Find a
8.91 Refer to Exercise 8.90. Suppose you wish to estimate (u) correct to within 0.2, with probabil- ity equal to 0.95. If you plan to use equal sample sizes, how large should n, and n be?
8.93 Refer to Exercise 8.92. How large a sample is required if you wish to estimate p correct to within 0.025, with probability equal to 0.90?
8.94 Independent random samples of n = 40 and n=80 observations were selected from binomial popu- lations 1 and 2, respectively. The number of successes in the two samples were x = 17 and x2 = 23.
8.95 Refer to Exercise 8.94. Suppose you wish to estimate (p1 - p) correct to within 0.06, with probability equal to 0.99, and you plan to use equal sample sizes that is, n = n2. How large should n
8.96 Ethnic Cuisine Ethnic groups in North America buy differing amounts of various food prod- ucts because of their ethnic cuisine. Asians buy fewer canned vegetables than do other groups, and
8.97 Women on Wall Street Women on Wall Street can earn large salaries, but may need to make sacrifices in their personal lives. In fact, many women in the securities industry have to make
8.98 Smoking and Blood Pressure An experiment was conducted to estimate the effect of smoking on the blood pressure of a group of 35 cigarette smokers. The difference for each participant was
8.99 Blood Pressure, continued Using a confi- dence coefficient equal to 0.90, place a confidence interval on the mean increase in blood pressure for Exercise 8.98.
8.100 lodine Concentration Based on repeated measurements of the iodine concentration in a solution, a chemist reports the concentration as 4.614 moles/litre, with an "error margin of 0.006."a. How
8.101 Heights If it is assumed that the heights of men are normally distributed, with a standard devia- tion of 6 cm, how large a sample should be taken to be fairly sure (probability 0.95) that the
8.102 Chicken Feed An experimenter fed different rations, A and B, to two groups of 100 chicks each. Assume that all factors other than rations are the same for both groups. Of the chicks fed ration
8.103 Antibiotics You want to estimate the mean hourly yield for a process that manufactures an antibi- otic. You observe the process for 100 hourly periods chosen at random, with the results = 34
8.104 Cheese and Beer The average European has become accustomed to eating away from home, especially at fast-food restaurants. Partly as a result of this fast-food habit, the per-capita consumption
8.105 Healthy Eating Don't Americans know that eating pizza and french fries leads to being overweight? In an American Demographics article23, a survey of women who are the main meal preparers in
8.106 Sunflowers In an article in the Annals of Bot- any, a researcher reported the basal stem diameters of two groups of dicot sunflowers: those that were left to sway freely in the wind and those
8.107 Working in Retirement Research released by Investors Group shows that non-retired Canadians overwhelmingly say their physical health is better than their financial health (67%) and many may be
8.108 University Costs A university administra- tor wishes to estimate the average cost of the first year at a particular university correct to within $500, with a probability of 0.95. If a random
8.109 Quality Control A quality-control engineer wants to estimate the fraction of defectives in a large lot of film cartridges. From previous experience, he feels that the actual fraction of
8.110 Circuit Boards Samples of 400 printed circuit boards were selected from each of two production lines A and B. Line A produced 40 defectives, and line B produced 80 defectives. Estimate the
8.111 Circuit Boards II Refer to Exercise 8.110. Suppose 10 samples of n = 400 printed circuit boards were tested and a confidence interval was constructed for p for each of the ten samples. What is
8.112 Ice Hockey The ability to accelerate rapidly is an important attribute for an ice hockey player. G. Wayne Marino investigated some of the variables related to the acceleration and speed of a
8.113 Ice Hockey II Exercise 8.112 presented sta- tistics from a study of fast starts by ice hockey skaters. The mean and standard deviation of the 69 individual average acceleration measurements
8.114 Ice Hockey III The mean and standard devia- tion of the speeds of the sample of 69 skaters at the end of the 6 m distance in Exercise 8.112 were 5.753 and 0.892 (m/sec) respectively.a. Find a
8.115 Student Loan Debt In a study done, the inci- dence of university student loan debt in Alberta was found to be 48.6% as compared to the national average of 42%.27 The amount of student debt
8.116 Recidivism An experimental rehabilitation technique was used on released convicts. It was shown that 79 of 121 men subjected to the technique pursued useful and crime-free lives for a
8.117 Specific Gravity If 36 measurements of the specific gravity of aluminum had a mean of 2.705 and a standard deviation of 0.028, construct a 98% confidence interval for the actual specific
8.118 Audiology Research In a study to establish the absolute threshold of hearing, 70 male first-year university students were asked to participate. Each sub- ject was seated in a soundproof room
8.119 Right-or Left-Handed A researcher classi- fied his subjects as innately right-handed or left-handed by comparing thumbnail widths. He took a sample of 400 men and found that 80 men could be
8.120 The Citrus Red Mite An entomologist wishes to estimate the average development time of the citrus red mite correct to within 0.5 day. From previous experiments it is known that or is in the
8.121 The Citrus Red Mite, continued A grower believes that one in five of his citrus trees are infected with the citrus red mite, mentioned in Exercise 8.120. How large a sample should be taken if
1. Verify the margin of error of 2.2 percentage points given by the survey designers for the full sample of 2000 adults. Find the margin of error for the two split samples of 1000 adults. What
2. Do the numbers reported in the table represent the number of people who fell into those categories? If not, what do those numbers represent?What elements, if any, go into a Canadian "national
3. When the set of questions on pride in Canada were asked, the pollster rotated the order of things and events given to the respondent. Why do you suppose this tech- nique was used?What elements, if
4. Construct 95% confidence intervals for the proportion of Canadians who:a. report that they were "proud" when Canada decided to not participate in the war on Iraq.b. report that they were "not
5. Compare the percentage of people in the full sample of 2000 who say that mul- ticulturalism makes them proud to be Canadian with the percentage of those in the second split sample who say that
6. If these questions were asked today, would you expect the responses to be similar to those reported here or would you expect them to differ substantially?What elements, if any, go into a Canadian
North York General Hospital, a multi-site community teaching hospital, gets approxi- mately 75,000 visits to its emergency department each year. With that many patients, Emergency was often very
A study reveals that interest among Canadian women in home and birthing centre delivery and in midwife care for women at low risk has been growing recently. In the past few years in Canada, several
7.48 A random sample of size n = 50 is selected from a binomial distribution with population proportion p = 0.7.a. What will be the approximate shape of the sampling distribution of p?b. What will be
7.62 Black Jack A gambling casino records and plots the mean daily gain or loss from five blackjack tables on an x chart. The overall mean of the sample means and the standard deviation of the
7.63 Brass Rivets A producer of brass rivets randomly samples 400 rivets each hour and calculates the proportion of defectives in the sample. The mean sample proportion calculated from 200 samples
7.64 Lumber Specs The manager of a building-supplies company randomly samples incoming lumber to see whether it meets quality specifications. From each shipment, 100 pieces of 2 x 4 lumber are
7.65 Coal Burning Power Plant A coal-burning power plant tests and measures three specimens of coal each day to monitor the percentage of ash in the coal. The overall mean of 30 daily sample means
7.66 Nuclear Power Plant The data in the EX0766 table are measures of the radiation in air particu- lates at a nuclear power plant. Four measurements were recorded at weekly intervals over a 26-week
7.67 Baseball Bats A hardwoods manufacturing plant has several different production lines to make baseball bats of different weights. One such produc- tion line is designed to produce bats weighing
7.68 Baseball Bats, continued Refer to Exercise 7.67 and suppose that during a day when the state of the 910-gram bat production process was unknown, the following measurements were obtained at
7.70 Refer to Exercise 7.69. Find the sampling distribution for x if random samples of size n = 3 are selected without replacement. Graph the sampling distribution of x.
7.71 Suppose a random sample of n = 5 observations is selected from a population that is normally distrib- uted, with mean equal to 1 and standard deviation equal to 0.36.a. Give the mean and
7.72 Batteries A certain type of automobile bat- tery is known to last an average of 1110 days with a standard deviation of 80 days. If 400 of these batteries are selected, find the following
7.59 Explain the difference between an x chart and a p chart.
7.49 A random sample of size n = 80 is selected from a binomial distribution with population proportion p = 0.25.a. What will be the approximate shape of the sampling distribution of p?b. What will
7.50a. Is the normal approximation to the sampling distribution of p appropriate when n = 400 and p = 0.8?b. Use the results of part a to find the probability that p is greater than 0.83.c. Use the
7.51 Road Trip! Parents with children list a GPS system (28%) and a DVD player (28%) as "must have" accessories for a road trip. 12 Suppose a sample of n = 1000 parents are randomly selected and
7.52 Fats and Sweets According to a study in the American Journal of Public Health, diets high in fat, sugar, and grains were associated with lower diet costs after adjustment for energy intakes,
7.53 Surfing the Net Do you use the Internet to gather information for a project? A survey reports that the per- centage of students who used the Internet as their major resource for a school project
7.54 M&Ms According to the M&M website, the average percentage of brown M&M candies in a pack- age of milk chocolate M&Ms is 13%.15 (This percentage varies, however, among the different types of
7.55 Measured Obesity Over the past several years, the prevalence of overweight and obese children and adolescents has risen, with the most substantial increases observed in economically developed
7.56 Oh, Nuts! Are you a chocolate "purist," or do you like other ingredients in your chocolate? American Demographics reports that almost 75% of consum- ers like traditional ingredients such as nuts
A statistical process control monitoring system samples the inside diameters of n = 4 bearings each hour. Table 7.6 provides the data for k = 25 hourly samples. Construct an x chart for monitoring
A manufacturer of ballpoint pens randomly samples 400 pens per day and tests each to see whether the ink flow is acceptable. The proportions of pens judged defective each day over a 40-day period are
7.73 Lead Pipes Studies indicate that drinking water supplied by some old lead-lined city piping sys- tems may contain harmful levels of lead. An important study of the Boston water supply system
7.74 Biomass The total amount of vegetation held by the earth's forests is important to both ecologists and politicians because green plants absorb carbon dioxide. An underestimate of the earth's
7.89 Canned Tomatoes During long pro- duction runs of canned tomatoes, the average weights (in mL) of samples of five cans of standard- grade tomatoes in puree form were taken at 30 control points
7.90 Pepsi or Coke? The battle for consumer preference continues between Pepsi and Coke. How can you make your preferences known? There is a webpage where you can vote for one of these colas if you
7.91 Strawberries An experimenter wants to find an appropriate temperature at which to store fresh strawberries to minimize the loss of ascorbic acid. There are 20 storage containers, each with
7.92 Filling Pop Cans A bottler of soft drinks pack- ages cans in six-packs. Suppose that the fill per can has an approximate normal distribution with a mean of 355 mL and a standard deviation of
7.93 Total Packing Weight Packages of food whose average weight is 454 grams with a standard deviation of 17 grams are shipped in boxes of 24 packages. If the package weights are approximately
7.94 Electronic Components A manufacturing process is designed to produce an electronic compo- nent for use in small portable television sets. The components are all of standard size and need not
1. To evaluate the results of Seligman's Monte Carlo experiment, first find the prob- ability distribution of the gain x on a single $5 bet.The technique of simulating a process that contains random
2. Find the expected value and variance of the gain x from part 1. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is
3. Find the expected value and variance for the evening's gain, the sum of the gains or losses for the 200 bets of $5 each. The technique of simulating a process that contains random elements and
4. Use the results of part 2 to evaluate the probability of 7 out of 365 evenings result- ing in a loss of the total $1000 stake. The technique of simulating a process that contains random elements
5. Use the results of part 3 to evaluate the probability that the largest evening's win- nings were as great as $1160. The technique of simulating a process that contains random elements and
Canada's profile in the international physics community got a huge boost as renowned "superstar" cosmologist Stephen Hawking (shown in the photo below floating on a zero-gravity jet) accepted a
7.88 Light bulbs, again Refer to Exercise 7.86. During a given week the number of defective bulbs in each of five samples of 100 were found to be 2, 4, 9, 7, and 11. Is there reason to believe that
7.87 Light bulbs, continued A hardware store chain purchases large shipments of light bulbs from the manufacturer described in Exercise 7.86 and speci- fies that each shipment must contain no more
7.75 Hard Hats The safety requirements for hard hats worn by construction workers and others, estab- lished by the American National Standards Institute (ANSI), specify that each of three hats pass
7.76 Imagery and Memory A research psycholo- gist is planning an experiment to determine whether the use of imagery picturing a word in your mind- affects people's ability to memorize. He wants to
7.77 Child Abuse A study of nearly 2000 women included questions dealing with child abuse and its effect on the women's adult life. The study reported on the likelihood that a woman who was abused as
7.78 Sprouting Radishes A biology experiment was designed to determine whether sprouting radish seeds inhibit the germination of lettuce seeds. Three 10-centimetre petri dishes were used. The first
7.79 Canadian Identity Do Canadians see them- selves as Canadians, as a province, or equally as a Canadian and a province? According to Strategic Counsel who presented the findings of the Globe and
7.80 Telephone Service Suppose a telephone com- pany executive wishes to select a random sample of n = 20 (a small number is used to simplify the exer- cise) out of 7000 customers for a survey of
7.81 Rh-Positive The proportion of individuals with an Rh-positive blood type is 85%. You have a random sample of n = 500 individuals.a. What are the mean and standard deviation of p, the sample

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