Edexcel As And A Level Modular Mathematics Statistics 1 1st Edition Keith Pledger Et Al - Solutions

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Refer to Question 4.Reword each question so it avoids the seven pitfalls.
2 applies to each of the following potential survey questions:*a. Do you support banning prayers in schools so that teachers have more time to spend teaching?b. Do you agree that marijuana should be legal?c. Studies have shown that consuming one alcoholic drink daily helps reduce heart disease. How
Explain which (one or more) of the seven pitfalls listed in Section
Give an example of a survey question that isa. Most appropriately asked as an open questionb. Most appropriately asked as a closed question
Give an example of a survey question that isa. Deliberately biasedb. Unintentionally biasedc. Unnecessarily complexd. Likely to cause respondents to lie
Give an example of a measure that is*a. Valid and categorical*b. Reliable but biased*c. Unbiased but not reliable
Find an example of a statistical study reported in the news for which information about one of the Seven Critical Components is missing. Write two hypothetical reports addressing the missing component that would lead you to two different conclusions about the applicability of the results of the
Explain how you would design and carry out a study to find out how students at your school feel about an issue of interest to you. Be explicit enough that someone would actually be able to follow your instructions and implement the study.Be sure to consider each of the Seven Critical Components
Scientists publish their findings in technical magazines called journals. Most university libraries have hundreds of journals available for browsing, many of them accessible electronically. Find out where the medical journals are located.Browse the shelves or electronic journals until you find an
An advertisement for a cross-country ski machine, NordicTrack, claimed, “In just 12 weeks, research shows that people who used a NordicTrack lost an average of 18 pounds.” Explain how each of the following components should have been addressed if the research results are fair and unbiased.a.
Moore (1991, p. 19) reports the following contradictory evidence: “The advice columnist Ann Landers once asked her readers, ‘If you had it to do over again, would you have children? She received nearly 10,000 responses, almost 70%saying ‘No!’. . . A professional nationwide random sample
Holden (1991, p. 934) discusses the methods used to rank high school math performance among various countries. She notes that “According to the International Association for the Evaluation of Educational Achievement, Hungary ranks near the top in 8th-grade math achievement. But by the 12th grade,
Suppose a study were to find that drinking coffee raised cholesterol levels. Further, suppose you drink two cups of coffee a day and have a family history of heart problems related to high cholesterol. Pick three of the Seven Critical Components and discuss why knowledge of them would be useful in
Explain why news reports should give the extent or size of the claimed effects or differences from a study instead of just reporting that an effect or difference was found.
In most studies involving human participants, researchers are required to fully disclose the purpose of the study to the participants. Do you think people should always be informed about the purpose before they participate? Explain.
Version 1 is that 25% of nonusers quit, whereas 50% of users quit. Version 2 is that 1% of nonusers quit, whereas 2% of users quit.
Version 1 is that the nicotine patch users were lung cancer patients, whereas the nonusers were healthy. Version 2 is that participants were randomly assigned to use the patch or not after answering an advertisement in the newspaper asking for volunteers who wanted to quit smoking.*b. Component
Suppose a study were to find that twice as many users of nicotine patches quit smoking than nonusers. Suppose you are a smoker trying to quit. Which version of an answer to each of the following components would be more compelling evidence for you to try the nicotine patches? Explain.*a. Component
Suppose a tobacco company is planning to fund a telephone survey of attitudes about banning smoking in restaurants. In each of the following phases of the survey, should the company disclose who is funding the study? Explain your answer in each case.a. When respondents answer the phone, before they
Refer to Case Study 1.1, “Heart or Hypothalamus?” Discuss each of the following components, including whether you think the way it was handled would detract from Salk’s conclusion:a. Component 3b. Component 4c. Component 5d. Component 6
Is it necessary that “data” consist of numbers? Explain.
Many research organizations give their interviewers an exact script to follow when conducting interviews to measure opinions on controversial issues. Why do you think they do so?
The student who conducted the study in “Hypothetical News Article 1” in this chapter collected two pieces of data from each participant. What were the two pieces of data?
According to Cynthia Crossen (1994, p. 106): “It is a poller’s business to press for an opinion whether people have one or not. ‘Don’t knows’ are worthless to pollers, whose product is opinion, not ignorance. That’s why so many polls do not even offer a ‘don’t know’
A prison administration wants to know whether the prisoners think the guards treat them fairly. Explain how each of the following components could be used to produce biased results, versus how each could be used to produce unbiased results:*a. Component 2: The researchers who had contact with the
The April 24, 1997, issue of “UCDavis Lifestyle Newstips” reported that a professor of veterinary medicine was conducting a study to see if a drug called clomipramine, an anti-anxiety medication used for humans, could reduce “canine aggression toward family members.” The newsletter said,
Suppose that a television network wants to know how daytime television viewers feel about a new soap opera the network is broadcasting. A staff member suggests that just after the show ends they give two phone numbers, one for viewers to call if they like the show and the other to call if they
Find a newspaper or Web article that discusses a recent study involving statistical methods. Identify the study as either an observational study or a randomized experiment. Comment on how well the simple concepts discussed in this chapter have been applied in the study. Comment on whether the news
Design and carry out a study to test the proposition that men have lower resting pulse rates than women.
A newspaper headline read, “Study finds walking a key to good health: Six brisk outings a month cut death risk.” Comment on what type of study you think was done and whether this is a good headline.
Suppose the administration at your school wants to know how students feel about a policy banning smoking on campus. Because they can’t ask all students, they must rely on a sample.a. Give an example of a sample they could choose that would not be representative of all students.b. Explain how you
Suppose a researcher would like to determine whether one grade of gasoline produces better gas mileage than another grade. Twenty cars are randomly divided into two groups, with 10 cars receiving one grade and 10 receiving the other. After many trips, average mileage is computed for each car.a.
Suppose a study first asked people whether they meditate regularly and then measured their blood pressures. The idea would be to see if those who meditate have lower blood pressure than those who do not do so.*a. Explain whether this would be an observational study or a randomized experiment.*b. If
Sometimes television news programs ask viewers to call and register their opinions about an issue. One number is to be called for a “yes” opinion and another number for a “no” vote. Do you think viewers who call are a representative sample of all viewers? Explain.
National polls are often conducted by asking the opinions of a few thousand adults nationwide and using them to infer the opinions of all adults in the nation. Explain who is in the sample and who is in the population for such polls.
Give an example of a decision in your own life, such as which route to take to school, for which you think statistics would be useful in making the decision.Explain how you could collect and process information to help make the decision.
Suppose you have 20 tomato plants and want to know if fertilizing them will help them produce more fruit. You randomly assign 10 of them to receive fertilizer and the remaining 10 to receive none. You otherwise treat the plants in an identical manner.*a. Explain whether this would be an
Suppose the officials in the city or town where you live would like to ask questions of a “representative sample” of the adult population. Explain some of the characteristics this sample should have. For example, would it be sufficient to include only homeowners?
Refer to Case Study 1.3, in which two students were accused of cheating because the licensing board determined the odds of such similar answers were less than 1 in 10,000. Further investigation revealed that over 20% of all pairs of students had matches giving low odds like these (Klein, 1992, p.
Universities are sometimes ranked for prestige according to the amount of research funding their faculty members are able to obtain from outside sources.Explain why it would not be fair to simply use total dollar amounts for each university, and describe what should be used instead.
Suppose researchers want to know whether smoking cigars increases the risk of esophageal cancer.*a. Could they conduct a randomized experiment to test this? Explain.*b. If they conducted an observational study and found that cigar smokers had a higher rate of esophageal cancer than those who did
Suppose you have a choice of two grocery stores in your neighborhood. Because you hate waiting, you want to choose the one for which there is generally a shorter wait in the checkout line. How would you gather information to determine which one is faster? Would it be sufficient to visit each store
A psychology department is interested in comparing two methods for teaching introductory psychology. Four hundred students plan to enroll for the course at 10:00 A.M. and another 200 plan to enroll for the course at 4:00 P.M. The registrar will allow the department to teach multiple sections at
Refer to Case Study1.1. When Salk measured the results, he divided the babies into three groups based on whether they had low (2510 to 3000 g), medium(3010 to 3500 g), or high (3510 g and over) birthweights. He then compared the infants from the heartbeat and silent nurseries separately within each
“If you have borderline high blood pressure, taking magnesium supplements may help, Japanese researchers report. Blood pressure fell significantly in subjects who got 400–500 milligrams of magnesium a day for four weeks, but not in those getting a placebo” (USA Weekend, 22–24 May 1998, p.
Explain what problems arise in trying to make conclusions based on a survey mailed to the subscribers of a specialty magazine. Find or construct an example.
Explain why the number of people in a sample is an important factor to consider when designing a study.
“People who often attend cultural activities, such as movies, sports events and concerts, are more likely than their less cultured cousins to survive the next eight to nine years, even when education and income are taken into account, according to a survey by the University of Umea in Sweden”
Explain why the relationship shown in Table 1.1, concerning the use of aspirin and heart attack rates, can be used as evidence that aspirin actually prevents heart attacks.
15 students do a mathematics test. Their marks are shown opposite. a Find the value of the median. 7 4 9 10 5 29 12 11 8 737 683b. Find Q and Q c Work out the interquartile range.AppendixLO1
A group of workers were asked to write down their weekly wage. The wages were: 550 400 260 320 500 450 a Work out the range for these wages. b Find Q and Q. 460 480 510 490 505 c Work out the interquartile range. Number of hours Cumulative Frequency frequency 0 25 1 10 2 20 3 10 4 25 5 10
A superstore records the number of hours overtime worked by their employees in one particular week. The results are shown in the table. a Fill in the cumulative frequency column and work out how many employees the superstore had in that week. b Find Q, and Q3. c Work out the interquartile
A moth trap was set every night for five weeks. The number of moths caught in the trap was recorded. The results are shown in the table. Number of moths Frequency 7 2 8 5. 9 9 10 14 11 5 Find the interquartile range.AppendixLO1
The weights of 31 Jersey cows were recorded to the nearest kilogram. The weights are shown in the table. Weight of cattle (kg) Frequency Cumulative frequency 300-349 3 350-399 6. 400-449 10 450-499 7 500-549 5 a Complete the cumulative frequency column in the table. b Find the lower quartile, Q c
The number of visitors to a hospital in a week was recorded. The results are shown in the table. Number of visitors Frequency 500-1000 10 1000-1500 25 1500-2000 15 2000-2500 5 2500-3000 5 Giving your answers to the nearest whole number find: a the lower quartile Qu b the upper quartile Qu e the
The lengths of a number of slow worms were measured, to the nearest mm. The results are shown in the table. a Work out how many slow worms. were measured. b Find the interquartile range for the lengths of the slow worms. Lengths of slow worms (mm) 125-139 140-154 Frequency 4 4 155-169 2 170-184 7
A gardener counted the peas in a number of pea pods. The results are shown in the table. Number Frequency of peas Cumulative frequency 6 8 7 12 8 36 9 18 10 15 11 10 a Complete the cumulative frequency column. b Calculate the 80th percentile. e Calculate the 40th percentile d Calculate the 65th
A shopkeeper goes to a clothes fair. He records the costs of jeans. The costs are shown in the table. Cost of jeans (E's) Frequency Cumulative frequency 10-15 11 16-20 35 21-25 34 26-30 16 31-35 10 36-40 5 a Complete the cumulative frequency table. b Calculate Pa c Calculate Po d Calculate the 20%
The table shows the monthly income for a number of workers in a factory. Calculate the 34% to 66% interpercentile range. Monthly income ('s) Frequency 900-1000 3 1000-1100 24 1100-1200 28 1200-1300 15 AppendixLO1
A train travelled from Lancaster to Preston. The times, to the nearest minute, it took for the journey were recorded over a certain period. The times are shown in the table. Time for journey (minutes) 15-16 17-18 19-20 21-22 Frequency 5 10 35 10 Calculate the 5% to 95% interpercentile
A roadside assistance firm kept a record over a week of the amount of time, in minutes, people were kept waiting for assistance in a particular part of the country. The time taken was from the time the phone call was received to the arrival of the breakdown mechanic. The times are shown below. Time
Given that for a variable x: 24 Find: Ex-78 11-8 b The variance o a The mean. The standard deviation o AppendixLO1
Ten collie dogs are weighed (w kg). The following summary data for the weights are shown below: w=241 w=5905 Use this summary data to find the standard deviation of the collies' weights.AppendixLO1
Eight students' heights (h cm) are measured. They are as follows: 165 170 190 180 175 185 176 a Work out the mean height of the students. 184 b Given h 254 307 work out the variance. Show all your working. e Work out the standard deviation. 4 For a set of 10 numbers: x-50 x-3 10 AppendixLO1
For a set of 15 numbers: = 86 = 568 Find the mean and the standard deviation of the combined set of 25 numbers.AppendixLO1
The number of members (m) in six scout groups was recorded. The summary statistics for these data are: m-150 m-3846 a Work out the mean number of members in a scout group. b Work out the standard deviation of the number of members in the scout groups.AppendixLO1
There are two routes for a worker to get to his office. Both the routes involve hold ups due to traffic lights. He records the time it takes over a series of six journeys for each route. The results are shown in the table. Route 1 15 15 11 17 14 12 Route 2 11 14 17 15 16 11 a Work out the mean time
For a certain set of data: 1975 fx-52325 Work out the variance for these data.AppendixLO1
For a certain set of data fx-264 fx-6456 -100 -12 Work out the standard deviation for these data.AppendixLO1
Nahab asks the students in his year group how much pocket money they get per week. The results, rounded to the nearest pound, are shown in the table. Number of Number of fx E's (x) students f 8 14 9 8 10 28 11 15 12 20 2 Totals a Complete the table. b Using the formulaff work out the variance for
In a student group, a record was kept of the number of days absence each student had over one particular term. The results are shown in the table. Number days Number of absent (x) fx students f 0 12: 1 20 2 10 3 7 4 5 fx a Complete the table. b Calculate the variance for these data. c Work out the
A certain type of machine contained a part that tended to wear out after different amounts of time. The time it took for 50 of the parts to wear out was recorded. The results are shown in the table. Lifetime in hours 5 AppendixLO1
The heights (x cm) of a group of 100 women were recorded. The summary data is as follows: 17 100 fx-2926225 Work out the variance and the standard deviation.AppendixLO1
a Work out the standard deviation of the following data. x 11 11 13 13 15 20 25 b Use the following coding to find the standard deviation of the data. Show all the working. ix-10 ii x 10 iii x-3 2 AppendixLO1
Use the following codings to find the standard deviation of the following weights, w. W 210 260 310 360 410 W ii w - 200 iii 10 w-10 200 3 a AppendixLO1
The coding y x-50 28 gives a standard deviation of 0.01 for y. Work out the standard deviation for x. h b The coding y produced a standard deviation for y of 0.045. What is the standard deviation of h?AppendixLO1
The coding y=x-14 produced a standard deviation for y of 2.37. What is the standard deviation of x? d The coding y=-5, 10 produced a standard deviation for y of 0.65. What is the standard deviation of s? The coding y=x-40 gives a standard deviation for y of 2.34. Write down the standard deviation
The lifetime, x, in hours, of 70 light bulbs is shown in the table. Lifetime in Number of light bulbs hours 20-22 3 22-24 12 24-26 40 26-28 10 28-30 5 total. 70 Using the coding y x-1 estimate the standard deviation of the actual lifetime in hours of 20 a light bulb.AppendixLO1
The weekly income, i, of 100 women workers was recorded. i-90 The data were coded using y=100 and the following summations were obtained. = 131, = 176.84 Work out an estimate for the standard deviation of the actual women workers' weekly income.AppendixLO1
For the set of numbers: 25389 10 3 2 15 10 5 7 675 a work out the median, b work out the lower quartile, e work out the upper quartile, d work out the interquartile range.AppendixLO1
A frequency distribution is shown below Class interval 1-20 21-40 41-60 61-80 81-100 Frequency (f) 5 10 15 12 8 Work out the interquartile range.AppendixLO1
A frequency distribution is shown below. Class interval 1-10 11-20 21-30 31-40 41-50 Frequency (f) 10 20 30 24 16 a Work out the value of the 30th percentile. b Work out the value of the 70th percentile. e Calculate the 30% to 70% interpercentile range.AppendixLO1
The heights(h) of 10 mountains were recorded to the nearest 10m and are shown in the table below. h1010 1030 1050 1000 1020 1030 1030 1040 1020 1000 Use the coding y-10 to find the standard deviation of the heights. 100 AppendixLO1
The times it took a random sample of runners to Time taken complete a race are summarised in the table. (t minutes) Frequency a Work out the lower quartile. 20-29 5 b Work out the upper quartile.) 30-39 10 c Work out the interquartile range. The mid-point of each class was represented by x and its
20 birds were caught for ringing. Their wing spans (x) were measured to the nearest centimetre. The following summary data was worked out: = 316 = 5078 a Work out the mean and the standard deviation of the wing spans of the 20 birds. One more bird was caught. It had a wing span of 13 centimetres b
The heights of 50 clover flowers are summarised in the table. Heights in mm (h) Frequency 90-95 5 95-100 10 100-105 26 105-110 8 110-115 1 a Find Q. b Find Q. c Find the interquartile range. d Use fx 5075 and fx2 516112.5 to find the standard deviation.AppendixLO1
A group of thirty college students was asked how many DVDs they had in their collection. The results are as follows. 12 25 34 17 12 18 29 34 45 6 15 925 23 29 22 20 32 15 15 19 12 26 27 27 32 35 42 26 25 Draw a stem and leaf diagram to represent these data. a Find the median. b Find the lower
The following stem and leaf diagram shows some information about the marks gained by a group of students in a statistics test. stem leaf 0 89 Key: 23 means 23 marks (2) 1 25 59 2 36 6 6 7 3 4 4 5 7 7 7779 4 5889 (9) (4) a Work out how many students there were in the group. b Write down the highest
The number of laptops sold by a store was recorded each month for a period of 26 months. The results are shown in the stem and leaf diagram. Key: 18 means 18 laptops stem leaf 1. 8 2 3 6 79 9 3 26667 88 4 4 5 5 5 7 7 7 7 9 5 2 7 7 9 (1) (5) a Find the median. b Find the lower quartile. c Find the
A class of 16 boys and 13 girls did a Physics test. The test was marked out of 60. Their marks are shown below. Boys Girls 45 54 32 60 26 54 47 32 28 34 54 56 34 34 45 46 32 29 47 48 39 52 24 28 44 45 56 57 33 a Draw a back-to-back stem and leaf diagram to represent these data. b Comment on your
The following stem and leaf diagram shows the weekend earnings of a group of college students. Males 8 765 Females Key: 5|1|0 means 15 for males 0 6 and 10 for females 1055588 2 5 5 8 8 9 88555 3 5 5 85 4 0 999866 a Write down the number of male students and the number of female students. b Write
Some data are collected. The lower quartile is 46 and the upper quartile is 68. An outlier is an observation that falls either 1.5 x (interquartile range) above the upper quartile or 1.5 x (interquartile range) below the lower quartile. Work out whether the following are outliers using this rule. a
Male and female turtles were weighed in grams. For males, the lower quartile was 400 g and the upper quartile was 580 g. For females, the lower quartile was 260 g and the upper quartile was 340 g. An outlier is an observation that falls either 1 x (interquartile range) above the upper quartile or 1
A group of students took a statistics test. The summary data for the percentage mark gained by boys and by girls is shown in the box plots opposite. a Write down the percentage mark which 75% of the girls scored more than. b State the name given to this value. c Compare and contrast the results of
Male and female turtles were weighed in grams. Their weights are summarised in the box plots opposite. a Compare and contrast the weights of the male and female turtles. b A turtle was found to be 330 grams in weight. State whether it is likely to be a male or a female. Give a reason for your
The heights of a year group of children were measured. The data are summarised in the group frequency table. Height (cm) Frequency Class width Frequency density 135-144 40 10 145-149 40 5 150-154 75 155-159 65 160-174 60 a Copy and complete the table. b Draw a histogram for these data.AppendixLO1
Some students take part in an obstacle race. The time it took each student to complete the race was noted. The results are shown in the histogram.a Give a reason to justify the use of a histogram to represent these data. The number of students who took between 60 and 70 seconds is 90. b Find the
The time taken for each employee in a company to travel to work was recorded. The results are shown in the histogram.The number of employees who took less than 10 minutes to travel to work is 48. a Find how many employees took less than 15 minutes to travel to work. b Estimate how many employees
A Fun Day committee at a local sports centre organised a throwing the cricket ball competition. The distance thrown by every competitor was recorded. The data were collected and are shown in the histogram. The number of competitors who threw less than 10 m was 40. a Why is a histogram a suitable
A farmer weighed a random sample of pigs. The weights were summarised in a grouped frequency table and represented by a histogram. One of the classes in the grouped frequency distribution was 28-32 and its associated frequency was 32. On the histogram the height of the rectangle representing that

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Edexcel As And A Level Modular Mathematics Statistics 1 1st Edition Keith Pledger Et Al - Solutions

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