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 Bottles of popular cola drinks are supposed to contain 300ml of cola. There is some variation from bottle to bottle because the filling mackinery is not perfectly precise. the distribution fo the contents is normal with SD=3ml. The result of the average is 299.03. Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300ml?(Find the z) A coin is tossed 10 times. What is the chance of observing 6 heads? Find the area under the x^2 curve with 10 degrees of freedom from the right of 4.86. A die is rolled 1296 times and lands on heads 650 times. Find the Z-value if it was expected to land on heads 600 times. A sample of 1,000 from a university says that 59% of students live on campus while 41% live off campus. Range from _____ to _____ is a 95% confidence interval for the students who live off campus. Scientist found orange juice helps reduce heart disease. People don't drink orange juice have 80% chance of heart disease. People who drink orange juice have 65% in a sample of 100 and SD = 4.1 Null hypothesis says orange juice doesn't help. The ave test score of students is 60. A sample of five students has ave test score of 75 with help of tutors. SD = 3.2 Null hypothesis : tutor doesn't help, ave score is still 60 In a sample of 40, ave age in 12th grade of school A = 17 SD = 0.2 In a sample of 20, ave age in 12 th grade of school B = 19 SD = 0.5 What is the SE for difference? What is the SE for a box with 60 red marbles, and 90 blue ones The average weight of the girls in the high school is 130lbs, and the SD is 30. Their average height is 70 inches, and the SD is 3. r=0.48 For a person who weight 148lbs will probably have height of __? The following distribution is given: Ave x=185 SDx=80 Ave y=120 SDy=45 r=-.75 Suppose y=170. What is the regression estimate for predicting the value of x from that of y? There has been a study which relates the scores of math and biology classes. The results of average test scores and SD's for each class are as follows: Ave Math score - 65 Ave Biology score - 70 SD - 5 SD - 10 r - .6 If a student has an average score of 70 in math, predict his biology score. In our Math 108 class the midterm scores average was about 55 with an SD of 20, as do scores on the final. The correlation between midterm scores and final scores is about 0.75. Estimate the average final score for the students whose midterm scores were 75. A study was done in Rye High School for the heights and weights of girls at the age of 16. The average weight was 110lbs with an SD of 10lbs and the average height was 64 inches with an SD of 2 inches. The correlation coeficient is 0.80. Predict the weight for a 16 year old girl whose height is 70 inches. The correlation between mid term and final is 0.8. The scatter diagram is football-shaped. Predict the percentile rank on the final for people rank 95% on mid term. A survey was conducted to estimate the correlation between teen Weed- Smokers and teen Tabacco- Smokers. The Weed- Smoker, puffed, on average 10 Weed- cigarettes per week with an SD of 2.Tabacco - Smokers smokes an average of 60 cigarettes per week with an SD of 5. Estimate the average Tabacco - Cigarettes smoked per week for a teen who smokes 12 Weed- Cigarettes. The correlation coefficient is 0.7. In a football- shaped diagram, for values X under 140 what is the percent of Y over 120? Use the following information. AveY=100,SDY=9. AveX=150,SDX=20. r=0.7. If r=0.5 for expected salary and educational level, what is the expected salary for people at the average educational level. salary avg=30,000, SD=10,000. educational level=12 yrs, SD=4 yrs. Find the error for this data: avgX=90, SD=7, avgY=70, SD=5, r=0.6. Wal-Mart sold 12,000 X-mas Trees in '97 w/ an SD of 300 in each of its stores. The sale of lights totaled to be 11,000 has the same SD. r=0.9, How many lights does it sell if one particular store sold 15,000 X-Mas trees. A school is working on the relationship between SAT and the first year greade. Ave SAT score=1160, SD=18. Ave first yera=83, SD=6, r=0.6 Find the R.M.S. Error. The results midway through a new weight loss program for women showed an average weight loss of 45 lbs, with an SD of 20. The final results showed an average weight loss of 50 lbs, with an SD of 10. The correlation between midpoint and final results was .6 For each member of this program, the final weight loss was predicted from the midpoint weight loss using the regression line. Compute the r.m.s. error for regression. A study was done to see if a person's parent's income had any effect on his or her own income. These were the results: Ave Parents income - 67,000 Ave Child's income - 58,000 SD - 15,000 SD - 10,000 r - .8 Compute the R.M.S. Error from the parent's income. The Albany Research Committee conducted a study on students that attend the Albany School District. The average height of students age 7 was about 3ft. 7 inches; the SD is 1.4. The average height of students age 17 is about 5ft. 8 inches; the SD is 2.3 inches. The r=0.68. Find the r.m.s. error for the regression of the height at 17 from the height at 7. The average weight of women at age 18 is 120 with an sd of 4. The average weight for women at age 21 is 137 with an sd of 6. With the r being equal to .4, compute the rms error for regression of weights at age 18 from weights at age 21. There were scores taken on the students of Suny Albany in the Business Law midterm and final. The average score on the midterm was 70 with an SD of 20. The average score on the final was 75 with an SD of 15, and the correlation coeficient was 0.60. Find the r.m.s. error for the regression line predicting midterm from final. ave weight = 130 lb SD = 10 lb ave height = 5'5" SD = 1.5" Compute the RMS error for regression of height from weight when r = 0.5. A shoe store is finding the relationship between teh heights and the shoe sizes. It is summarized as followers. Ave Height=75 inches, SD=5 Ave shoe size=8, SD=1.5, and r=0.45 Find the regression equation for predicting shoe size from the height. The following distribution is given: Ave x=185 SDx=80 Ave y=120 SDy=45 r=-.75 What is the slope of the regression line? The New York Knicks trainer has found a new jump training program to help players improve their vertical. The predicted improvement is 1inch per 25 hours of training, but the first 40 hours will have no results because it takes time for the body to adjust to the program. How many hours does a rookie need to spend on the program to improve his vertical 6 inches? The equation of regression line is y = 0.5x + 2. r = 0.7 ave of x value = 2, find equation of SD line. Suppose that both parents in a family carry genes for blood types A and B. The blood types of their children are independent and each child has probability 1/4 of having blood type A. there are 4 children in the family. Find the probability of two children having blood type A. You have a biased coin that lands heads 65% of the time and lands tails 35% of the time. You flip it 6 times. What is the probability you get exactly 5 heads? If a die is rolled 20 times, find the chance of getting exactly 4 aces. A roulette wheel has 38 numbers, including 0 and 00. What is the probability of 0 or 00 coming up in once 10 consecutive spins of the wheel? If a coin is tossed 5 times, what is the chance of observing 3 heads? A deck of shuffled card, draw 10 times with replacement. What is the probability of getting exactly one "King"? A coin is tossed 5 times, what is the chance of exactly two heads? A coin is tossed 10 times, what is the chance of 5 heads A factory is duirng a survey. A simple random sample of 2500 workers have 1400 female workers. Find the standard error for the percentage. 200 draws are made from a bag of 5 tickets. Each ticket was labelled individually with a number, as follows: 2 2 6 8 9 Compute the expected sum and standard error for sum. In a city of 50,000 a random sample of 1,000 was taken to measure yearly incomes. Of the sample, 500 earned 20,000 or less, 350 earned between 20,000 and 70,000 while 150 earned over 70,000. Find the SE for the percentage of residents who earn more than 70,000 dollars. There is a town of 50,000 people which has 30,000 of the population that are female. A survey of 500 people at randon from this town is taken. Find the S.E. for the percent of female in the sample. The Stanley Cup finals in 1994 were played in Madison Square Garden. There were 40,000 fans present, of which 500 were Vancouver fans. After the game, 100 lucky fans were invited into the locker rooms. What’s the expected value and standard error of Vancouver fans being drawn? A university has 15,000 students of whom 5,000 are girls. The registrar draws a simple random sample 500 students. Find the SE for the % of girls in the school. In a school there are 565 Male and 495 Female. A random sample of 100 is taken, what is the Standard Error of percentage of male in the sample? 49 draws from a box with an SD of 5. Find the SE for %. What is the SE for a box with no replacement. Box: 100 tickets , 20= draws, SD=6 A computer store is doing a survey for the brand that has better selling. They take a sample of 500 people out to obtain the percentage of people who preffered PPII over IBM. The result turn out 300 people prefferd PPII. Compute 95% confidence interval for the percentage of people who preferred PPII. There is a sample of High School of 5,000 students to see how many are involved in after school activities. From the sample of 500, 300 were involved in activities, while the remaining 200 were not. Find the 95% confidence interval for those students involved in sports. The University of Albany has about 50,000 students. A survey of 1,000 students shows that the average age is about 24.3 years and the SD to be 3.5 years. Fine a 95% C.I. for the average of all 50,000 students. A simple random sample of 1000 people is taken to estimate the percentage of Hispanics in a community of 20,000 people. It turns out that 400 people in the sample are Hispanics. Find a 99.7% confidence interval for the % of Hispanics among the 20,000 people in the community. 500 draws are pick at random from a box. The average of this box is 21 and the SD is 2.5. Find the average will likely to be off. You do a study to estimate the average and SD for a certain variable. With a simple random sample size of 225 from a population of 20000, your sample has an average of 10 and an SD of 4. Find a 95% confidence interval for the population average. A random sample is taken from a box containing 1,000 tickets. If a sample of 100 tickets is taken with replacement, find the average sum and standard error for the sample. 20 of the tickets were picked which had the number 1, 50 which had the number 2, and 30 which had the number 3. In a town there are 20,000 people. A survey is conducted of 400 people. The average age of the sample is 25.7 years, and the SD is 3.7 years. The average age of all the population is estimated as_______. This is likely to be of by_______or so. If 200 tickets are taken with replacement from the box containing the numbers: 2,3,5,7, and 9, what will the average of the draws be? How much chance variation is there in the average of # from the box: {0, 5, 10, 15, 20} with 10 draws and an SD of 7. There is a psyshology test designed to measure how accurately the subject appraises other people. The exam is given to different groups of people. the result for male and female students who are major in music are: Sex Total number average Standard Deviatiion Male 130 28.50 5.48 female 160 26.86 5.76 Find the z satistic. The Null Hypothesis says that the average for a certain variable should be 200. This is tested with a simple random sample of 900. The sample has an average of 204 and a SD of 60. Compute the Z-test statistic and P-Value. EAS' new weight loss product is tested. There are 75 people in the treatment group and 80 in the control group. At the end of the treatment, the average weight for the treatment group is 193 lbs with an SD of 20 lbs and the average weight for the control group is 200 lbs with an SD of 25 lbs. What is the standard error for a difference? In a city of 50,000 residents a survey of 500 was taken to find the average income for each household. The researcher believes that the average will be approximately 30,000 dollars per household. The actual average of the sample was 49,000 dollars with an SD of 500 dollars. Determine the P-value for the sample. A study was done to compare the difference in verbal and math scores on the SAT. A sample of 900 was taken for the Math test, and there was a recorded average of 600 with an SD of 90. A sample of 400 was taken for the verbal test, the recorded average was 550 with and SD of 80. What is the difference for the two tests? Data is taken form a box that 600 draws are taken at random. The Null Hypothesis says that the average of the box is 60. The alternativre says it is mor than 60. The results showed that the average was 63.2 and it has an Sd of 35. Compute the z. One hundred draws are make at random with replacement from box A containing 1 red marble and 1 blue marble. Independently 100 draws are make at random with replacement from box B containing 1 orange marble and 1 yellow marble. Find the SE for the differences between the number's of red marbles and the number's of orange marbles. The Yankees are trying to measure the effectiveness of their minor league system. They take a sample of 10 players from their double A and triple A affiliates. The sample of batters from double A hit an average of 12 home runs a season with a standard deviation of 2.5. The triple A sample hits an average of 14 home runs with a standard deviation of 3.1. What is the expected difference and standard error of the difference between the Yankees’ double A and triple A teams? A survey was taken in the death rates of two cities in Colombia, which were Cali and Medillin. In Cali out of a sample of 225 people the average death rate a day is 105 with and SD of 45, and in Medillin out of a sample of 144 people the average is 110 with an SD of 36. Find the standard error for the difference between these two averages. What is the Z-stat for this information: Avg=0, obs=50, 100 Draws, SD of 10. Find the area to the right of 5.5 under the chi-square table with 2 degrees of freedom A study is made to see if voting and gender are independent. 200 men and 100 women are polled to find out if they voted in the last election. The following data was obtained. Carry out the Chi-Square Test and compute the P-value. Men Women Voted 103 59 Didn't Vote 97 41 In this year's election, 50% of the votes were for the Republican candidate, 40% were for the Democratic candidate, and 10% were for the Independant. Drawing from the tickets in the box we observe 515 R, 370 D, and 115 I. What is the P-value, and is it statistically significant? Find the area under the X^2-curve with 8 degrees of freedom to the right of 2.73. A coin is tossed 100 times head = 70 times, tail = 30 times, null hypothesis says this coin is fair. In the New York Giant’s training camp, the average football player weighed 232 pounds with a standard deviation of 9. The average number of push-ups a player can do is 95 with a standard deviation of 11. The correlation of the number of push-ups a player can do on the weight of that player is -0.87. During pre-season, the Giants lose their star linebacker. They want to find a replacement for him. If they want a player who is 250 pounds, and in better shape then normal, how many push-ups should he be able to do? Last year, Mark Mcguire hit 70 home runs. The average starter only hit 19 with a standard deviation of 6. The average starter also batted .286 with a standard deviation of .017. The correlation of batting on home runs is 0.43. What percentage of starters hit 30 home runs or more and batted above .300? The World Boxing Federation wants to reduce the violence of heavyweight fights broadcasted on television. They want to know how many punches are thrown per round. They take a television sample of 200 rounds from different fights, and record the number of punches thrown. The average is 113, with a standard deviation of 31. The WBF wants to know whether the real average is under 120. The null hypothesis states that the real average is 120. The alternate hypothesis states that it is under 120. What is the p-value of the null? Every year, Spain has a very famous event known as “the Running of the Bulls”. Many tourists visit Spain and run alongside of the bulls. As a result, many people become injured. Last year, 145 people were hospitalized. Of those, 5 were Americans. Of the 75,000 people present, what is the 95% confidence interval of Americans at the event. GNC is introducing a new line of weightlifting devices. They want to do research on how much the average man who works out can bench press. There are 900,000 American men who work out. A sample of 1600 men is measured, and they can bench an average of 212 pounds with a standard deviation of 42. What is the 95% confidence interval for how much weight lifting men can bench? In a study of college students, their age averaged out to be 21 with an SD of 10. Using the normal curve what is the percentage of college students who older than 23. Last year, the I.Q.'s of entering college students averaged out to be 110, with an SD of 15. Using the normal curve, estimate the 80th percentile of the score distribution. The average of a statistics test is 66, with an SD of 7. Using the normal curve, estimate the percentage of test scores over 80. The percentage will be approximately 15.25 The percentage will be approximately 10.75 The percentage will be approximately 6.125 The percentage will be approximately 20 The percentage will be approximately 2.275

Carlos Rodriguez <carlos@math.albany.edu>
This problem was contributed by a student in Elementary Statistics. It is offered as it is with no warranty of any kind
Last modified: Wed May 13 12:29:11 EDT 1998