Sampling Techniques

Sampling Techniques Worksheet For each description of sampling, decide if the sampling technique is A. Simple Random B. Stratified C. Cluster D. Systematic E. Convenience 1. In order to estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Intel selected every 8th chip that comes off the assembly line starting with the 3rd, until she obtains a sample of 140 chips. 2. In order to determine the average IQ of ninth-grade students, a school psychologist obtains a list of all high schools in the local public school system.

She randomly selects five of these schools and administers an IQ test to all ninth-grade students at the selected schools. 3. In an effort to determine customer satisfaction, United Airlines randomly selects 50 flights during a certain week and surveys all passengers on the flights. 4. A member of Congress wishes to determine her constituency’s opinion regarding estate taxes. She divides her constituency into three income classes: low-income households, middle-income households, and upper-income households. She then takes a random sample of households from each income class. 5.

In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals form a list of known users of the product. 6. A radio station asks its listeners to call in their opinion regarding the use of American forces in peacekeeping missions. 7. A farmer divides his orchards into 50 subsections, randomly selects 4 and samples all of the trees within the 4 subsections in order to approximate the yield of his orchard. 8. A school official divides the student population into five classes: freshman, sophomore, junior, senior and graduate student.

The official takes random sample from each class and asks the members’ opinions regarding student services. 9. A survey regarding download time on a certain Web site is administered on the Internet by a market research firm to anyone who would like to take it. 10. A lobby has a list of 100 senators of the United States. In order to determine the Senate’s position regarding farm subsidies, they decide to talk to every seventh senator on the list starting with the third. Chapter 1 – Frequency Table construction The following table shows the number of arrivals at a Wendy’s restaurant during several 15-minute intervals. 6664 566114 27124 65537 22975 62657 68265 46985 Define the variable. X = Construct a Frequency table of the above data. Make sure you title each column and fill in each space. Answer the following questions using your frequency table. 1. What does the relative frequency column add to? Why is this so? 2. RF(X = 5) 2. RF(X > 5) = 3. RF(X < 5) = 4. RF(3 < X < 7) = Chapter 2 – Boxplot For each of the following sets of data a. construct a boxplot b. state which quarter has the largest spread and what that spread is c. state which quarter has the smallest spread and what that spread is d. ind the IQR e. determine if there are any outliers by identifying them 1. This data is a list of three-year rates of return of 40 small-capitalization growth mutual funds. 27. 416. 710. 824. 125. 9 12. 728. 522. 218. 417. 4 22. 629. 611. 645. 916. 6 32. 147. 710. 918. 423. 3 18. 23225. 523. 738. 1 23. 714. 712. 831. 121. 9 18. 421. 32719. 615. 8 14. 73719. 218. 529. 1 2. This data is a list of the percent of persons living in poverty in each of the 50 US states in 1997. 14. 89. 41310. 411. 216. 323. 415. 214. 112. 5 8. 510. 113. 316. 410. 710. 016. 611. 715. 10. 5 18. 89. 111. 618. 49. 79. 611. 811. 416. 717. 5 18. 414. 38. 210. 718. 67. 712. 311. 98. 38. 5 16. 814. 79. 69. 310. 69. 211. 813. 110. 912. 7 3. The following table gives the number of children under the age of five in 50 households. Number of children under fiveNumber of households 016 118 212 33 41 Chapter 2 – Measures of center, spread and location For each of the following sets of data find a. the average b. the standard deviation c. the first quartile d. the median e. the mode f. the third quartile g. the 90th percentile h. the 40th percentile 1.

This data is a list of three-year rates of return of 40 small-capitalization growth mutual funds. 27. 416. 710. 824. 125. 9 12. 728. 522. 218. 417. 4 22. 629. 611. 645. 916. 6 32. 147. 710. 918. 423. 3 18. 23225. 523. 738. 1 23. 714. 712. 831. 121. 9 18. 421. 32719. 615. 8 14. 73719. 218. 529. 1 2. This data is a list of the percent of persons living in poverty in each of the 50 US states in 1997. 14. 89. 41310. 411. 216. 323. 415. 214. 112. 5 8. 510. 113. 316. 410. 710. 016. 611. 715. 110. 5 18. 89. 111. 618. 49. 79. 611. 811. 416. 717. 5 18. 414. 38. 210. 718. 67. 712. 311. 98. 38. 5 16. 814. 79. 69. 10. 69. 211. 813. 110. 912. 7 3. The following table gives the number of children under the age of five in 50 households. Number of children under fiveNumber of households 016 118 212 33 41 Chapter 2 – Histogram The following is a frequency table of the number of customers who enter a Wendy’s restaurant in a 15-minute interval. Complete the Cumulative Frequency column. Number of customers FrequencyRelative FrequencyCumulative Frequency 110. 0250. 025 260. 15 310. 025 440. 1 570. 175 6110. 275 750. 125 820. 05 920. 05 1000. 0 1110. 025 Construct a histogram below. Make sure to label and scale both axis.

Chapter 2 – Worksheet The following is a frequency table of the number of customers who enter a Wendy’s restaurant in a 15-minute interval. Complete the Cumulative Frequency column. Number of customers FrequencyRelative FrequencyCumulative Frequency 110. 0250. 025 260. 15 310. 025 440. 1 570. 175 6110. 275 750. 125 820. 05 920. 05 1000. 0 1110. 025 1. a. the average b. the standard deviation c. the first quartile d. the median e. the mode f. the third quartile g. the 90th percentile h. the 40th percentile 2. a. Construct a boxplot b. state which quarter has the largest spread and what that spread is c. tate which quarter has the smallest spread and what that spread is d. find the IQR e. determine if there are any outliers by identifying them 3. Construct a histogram below. Make sure to label and scale both axis. Chapter 12 – Linear Regression For each of the following sets of data a. Identify the independent and dependent variable b. Make a scatterplot of the data on your calculator c. Find the least squares (best fit) line d. Define the physical interpretation of the slope of the least squares line e. Draw the least squares line on the same graph as the scatterplot f. Define the domain for the least squares line. . Determine if the least squares line is significant h. Use the least squares line to predict the values of the dependent variable from the independent variables given. 1. The data below represent the per capita gross domestic product of randomly selected countries in Western Europe and the life expectancy of the residents (according to the Time Almanac, 2000). CountryPer capita GDPLife Expectancy Austria21. 477. 48 Belgium23. 277. 53 Finland20. 077. 32 France22. 778. 63 Germany20. 877. 17 Ireland18. 676. 39 Italy21. 578. 51 Netherlands2278. 15 Switzerland23. 878. 99 United Kingdom21. 277. 37 2.

The following data is a comparison of diamond size, in carats, and purchase price. CaratsPrice, $ 0. 663282 0. 753950 0. 703543 0. 713788 0. 774108 0. 804378 0. 905682 0. 916462 1. 189362 Chapter 12 – Linear Regression Outliers For each of the following sets of data i. Determine if there are any outliers. 1. The data below represent the per capita gross domestic product of randomly selected countries in Western Europe and the life expectancy of the residents (according to the Time Almanac, 2000). CountryPer capita GDPLife Expectancy Austria21. 477. 48 Belgium23. 277. 53 Finland20. 077. 32 France22. 778. 63

Germany20. 877. 17 Ireland18. 676. 39 Italy21. 578. 51 Netherlands2278. 15 Switzerland23. 878. 99 United Kingdom21. 277. 37 2. The following data is a comparison of diamond size, in carats, and purchase price. CaratsPrice, $ 0. 663282 0. 753950 0. 703543 0. 713788 0. 774108 0. 804378 0. 905682 0. 916462 1. 189362 Chapter 3 – Probabilities 1. Suppose a single card is selected from a standard 52-card deck of playing cards. Let K = drawing a king Q = drawing a queen T = drawing a two R = drawing a red card a. Find P(K) b. Find P(K or Q) c. Find P(K and Q) d. Find P(K and R) e. Are events K and Q mutually exclusive?

Why or why not? 2. If P(A) = 0. 25 and P(B) = 0. 45, find the following a. P(A or B) if P(A and B) = 0. 15 b. P(A and B) if P(A or B) = 0. 6 c. P(A or B) if A and B are mutually exclusive d. P(A and B) if A and B are mutually exclusive e. P(A’) 3. If P(A) = 0. 60, P(A or B) = 0. 85 and P(A and B) = 0. 05, find P(B). 4. What is P(F|E) if P(E and F) = 0. 60 and P(E) = 0. 8? 5. Suppose that E and F are two events and that P(E and F) = 0. 24, P(E) = 0. 4) and P(F) = 0. 6. Are E and F independent events? Why? 6. Suppose that A and B are two events and that P(A and B) = 0. 3, P(A) = 0. 5 and P(B) = 0. . Are A and B independent events? Why? Chapter 3 – Tree Diagrams 1. Construct a tree diagram for the gender of the children in families with three children. Include the probabilities on the tree. a. Find the probability that a family will have all girls. b. Find the probability that a family will have 2 boys and 1 girl, order not important. c. Find the probability that a family will have first a girl and then 2 boys. d. Find the probability that a family will have 2 boys after having had a girl. 2. Suppose you have 5 blue cards numbered 1 through 5 and 8 yellow cards numbered 1 through 8.

Your experiment is to draw two cards, one at a time without replacement. a. Draw a tree diagram b. Find the probability of drawing two blue cards. c. Find the probability of drawing a blue card and a yellow card, order not important. d. Find the probability of drawing a yellow card first and then a blue card. e. Find the probability of drawing a blue card GIVEN that you drew a blue card on the first draw. 3. Repeat #2, with replacement. ? Chapter 3 – Contingency Tables. 1. Consider the following table of Level of Education versus marital status from the US. Census Bureau.

Marital StatusDid not graduate high schoolHigh School graduateSome CollegeCollege GraduateTOTAL Never married4012779065657685 Married, Spouse present15122360762700329811 Married, Spouse absent1877200614351489 Separated109415151214598 Widowed5000475722641456 Divorced2951704756493766 TOTAL Suppose a person is picked at random. (Leave answers in unreduced fractional form) a. Find P(the person picked had never been married) b. Find P(the person picked had Some College AND is separated) c. Find P(the person picked was a College graduate OR Widowed) d. Find P(the person picked was Divorced GIVEN the person did not graduate High School) e.

Find P(the person picked was a College graduate GIVEN the person never married) 2. Consider the following table which represents the size of a farm and the tenure of the operator (a full owner owns all the acreage farmed, a part owner owns some of the land and rents the rest, a tenant leases the land farmed). (from Statistical Abstract of the US, 2000) Size of farmFull ownerPart ownerTenantTOTAL Under 50 acres4605748 50-179 acres40913153 180-499 acres18916945 500-999 acres5010323 > 1000 acres4011422 TOTAL Suppose a farmer is picked at random. (Leave answers in unreduced fractional form. ) a.

Find P(the farmer picked is a Full owner) b. Find P(the farmer picked has 500-999 acres) c. Find P(the farmer picked is a Full owner AND has 180-499 acres) d. Find P(the farmer picked is a Tenant OR has 50-179 acres) e. Find P(the farmer picked is a part owner GIVEN the farmer has under 50 acres) f. Find P(the farmer picked has > 1000 acres GIVEN the farmer is a part owner) Chapter 4 – Poisson 1. A McDonald’s manager knows that cars arrive at the drive-through at a rate of 2 cars per minute between the hours of 12 noon and 1 pm. a. What is the expected number of cars to arrive between 12 noon and 12:05? . What is the probability that exactly 6 cars will arrive between 12 noon and 12:05? c. What is the probability that less than 6 cars will arrive between 12 noon and 12:05? d. What is the probability that at least 6 cars will arrive between 12 noon and 12:05? 2. The number of hits to a Web site follows a Poisson distribution, hits occur at a rate of 1. 4 per minute between 7 and 9 pm. Compute the probability that the number of hits to the Web site between 7:30 and 7:35 pm is a. exactly seven b. less than seven c. at least seven 3. Assuming ? = 7 compute P(X = 10) P(X < 10) P(X > 10) P(7 < X < 9)

Chapter 5 – Exponential Suppose the length of time (in hours) between emergency arrivals at a certain hospital is modeled as an exponential distribution with ? = 2. 1. What is being measured here? 2. In words, define the Random Variable X. X = ________________________________________________ 3. The interval of values for X is: ______________ 4. X ~ _________ 5. Write the probability density function: f(x) = _____________ 6. Find the probability that less than 3 hours pass without an emergency arrival. Sketch the graph. Shade the area of interest. Label both axes. b. Write the probability statement and find the probability.

P(_______) = ______ 7. Find the probability that at least 5 house pass without an emergency. Sketch the graph. Shade the area of interest. Label both axes. b. Write the probability statement and find the probability. P(_______) = ______ 8. Find the 40th percentile for length of time between emergency arrivals. Sketch the graph. Shade the area of interest. Label both axes. b. Write the probability statement and find the value of X. P(_______) = ______ Chapter 6 – Normal The height of 10-year-old males is known to be normally distributed with a mean of 55. 9 inches and standard deviation of 5. 7 inches.

Suppose one 10-year-old male is randomly drawn. a. Define the random variable in words. X = _______________________________ b. X~ ____(____, _____) c. Find the probability that the child is less than 53 inches tall. Draw a sketch of the situation and shade the area of interest. Write the probability statement and find the probability. P(________) = _________ d. Find the probability that the child is at least 56 inches tall. Draw a sketch of the situation and shade the area of interest. Write the probability statement and find the probability. P(________) = _________ e. Find the probability that the child is between 53 and 56 inches tall.

Draw a sketch of the situation and shade the area of interest. Write the probability statement and find the probability. P(________) = _________ f. Find the IQR for the height of 10-year-old males. Draw a sketch of the situation and shade the area of interest. Write the probability statement and find the IQR. P(___ < X < ____) = ________ IQR = _____ – _____ = _____ g. 60% of the children are at least how tall? Draw a sketch of the situation and shade the area of interest. Write the probability statement and find the height. P(___ _ ____) = ________ X = ________ Chapter 7 – Worksheet

The heights of pine seedlings grown by the State of Virginia have a uniform distribution with an average of 24. 5 inches and standard deviation of 1. 15 inches. Suppose a random sample of 20 pine seedlings is taken. a. Define the Random Variable, X, in words. X = _______________________________________________________ b. Define the Random Variable, , in words. = _______________________________________________________ c. ~ ____ (_____, _____) d. Find the probability that the average height of the 20 pine seedlings is between 24 and 25 inches. Write a probability statement, draw a graph, shade the desired area and find the probability. . Find that probability that the average height of the 20 pine seedlings is at least 25. 5 inches. Write a probability statement, draw a graph, shade the desired area and find the probability. f. Find the 85th percentile of the distribution of the average of the 20 pine seedling heights. Write a probability statement, draw a graph, shade the desired area and find the percentile. Chapter 8 – Error Bound of the Mean For each of the following. a. State the point estimate of the true mean. b. Construct a 92% confidence interval on the true mean. c. Define what the confidence interval means, in words. d.

Describe what happens to the confidence interval if you increase the sample size. e. Find the sample size required to estimate the mean price within $1000 with 90% confidence. 1. Suppose we are in the market to purchase a used Corvette. We take a random sample of 15 used Corvettes and obtain a sample mean of $38,247 and sample deviation of 7500 2. In 2000, as reported by ACT research Service, the mean ACT Math score was ? = 20. 7. The data for 20 students from High School A is below. Does the confidence interval generated from this data contain the true mean? 2423162625 2218252617 2827232123 2025211930 3.

A researcher is interested in the approximating the mean number of miles on three-year old Chevy Cavaliers. She finds a random sample of 35 Cavaliers in the Orlando, Florida area and obtains the following results. 3781520000571034658524822 496783098352969800039862 600065192342856090641841 3985143000743615266433857 5289645280300004171676315 2244245301528994152628381 5516351821365003197416529 Chapter 8 – Error Bound of the Proportion For the following, a. State the point estimate of the true proportion. b. Construct a 92% confidence interval on the true proportion. c. Define what the confidence interval means, in words. . Describe what happens to the confidence interval if you decrease the sample size. 1. In a Harris Poll conducted February 9, 2000, 1247 of 2208 ramdomly selected Americans said they judged that state law governing child safety restraints in vehicles should be strengthened. 2. A study of 74 patients with ulcers was conducted in which they were prescribed 40 mg of Pepcid. After 8 weeks, 58 reported confirmed ulcer healing. 3. The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 863 patients who received 10 mg doses of Lipitor daily, 47 reported a headache as a side effect.

Chapter 9 – Single Mean For each of the following a. State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. h. Construct a 95% confidence interval for the true mean from the sample data. i. State what a Type I error is. 1. In February of 2001, an executive of a major oil company claimed that the mean price of regular unleaded gasoline in Cook County, Illinois was exactly $1. 6. A member of the county board feels that the mean price is different from $1. 56. Below is a table of the samples the county board member gathered. Who’s right? 1. 521. 611. 551. 581. 66 1. 511. 581. 551. 581. 61 1. 581. 591. 571. 531. 59 1. 561. 611. 571. 651. 53 2. A sociologist claims that the mean age at which women marry in Memphis, Tennessee, is greater than the mean age of 25. 0 throughout the United States, on the basis of data from the Monthly Vital Statistics Report published by the Centers for Disease Control.

Based upon a random sample of 20 recently filed marriage certificates, she obtains the ages shown in the table below. Is she right? 4023302431 2928343534 2421462931 2929213339 Chapter 9 – Single Proportion For each of the following a. State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. h. Construct a 95% confidence interval for the true proportion from the sample data. i. State what a Type II error is. . The drug Lipitor is meant to reduce the total cholesterol and LDL-cholesterol. In clinical trials, 19 out of 863 patients taking 10 mg of Lipitor daily complained of flulike symptoms. Suppose that it is known that 1. 9% of patients taking competing drugs complain of flulike sumptoms. Is there significant evidence to support the claim that more than 1. 9% of Lipitor users experience flulike symptoms as a side effect? 2. In a survey conducted by the American Animal Hospital Association, 37% of respondents stated that they talk to their pets on the answering machine or telephone.

A veterinarian found this results hard to believe, so he randomly selected 150 pet owners and discovered that 54 of them spoke to their pet on the answering machine or telephone. Test the veterinarian’s claim that less than 37% of pet owners speak to their pets on the answering machine or telephone. Chapter 10 – Two means For each of the following a. State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. . State what the Type I error is 1. Researchers wanted to determine whether carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of one cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dished. The results are presented in the table below (measured in bacteria/cubic foot). Test the claim. Carpeted RoomsUncarpeted Rooms 11. 812. 1 8. 28. 3 7. 13. 8 137. 2 10. 812 10. 111. 1 14. 610. 1 413. 7 2. Researchers wanted to know whether there was a difference in comprehension among students learning a computer program based on the style of the text. They randomly divided 36 students into two groups of 18 each. The researchers verified that the 36 students were similar in terms of educational level, age and so on. Group 1 individuals learned the software using a visual manual while Group 2 learned the software using a textual manual. The following data represents scores the students received on an exam given to them after they studied from the manuals. Test the researchers claim.

Visual ManualTextual Manual 51. 0864. 55 57. 0357. 60 44. 8568. 59 75. 2150. 75 56. 8749. 63 75. 2843. 58 57. 0757. 40 80. 3049. 48 52. 2049. 57 60. 3556. 54 76. 6039. 91 70. 7765. 31 70. 1551. 95 47. 6049. 07 46. 5948. 83 81. 2372. 40 67. 3042. 01 60. 8261. 16 Chapter 10 – Two Proportions For each of the following a. State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. h. State what a Type II error is 1.

The drug Prevnar is a vaccine to prevent certain types of bacterial meningitis. It is typically administered to infants starting around two months of age. In randomized, double-blind clinical trials of Prevnar, infants were randomly divided into two groups. Subjects in Group1 received Prevnar while subjects in Group 2 received a control vaccine. After the first dose, 107 of 710 subjects in Group 1 experienced fever as a side effect. After the first dose, 67 of 611 subjects in Group 2 experienced fever as a side effect. Test the claim that a higher proportion of subjects in Group 1 experienced fever as a side effect. . On March 19-21, 1999, the Gallup Orgranization surveyed 535 adults ages 18 years old or older and asked “Do you think there is life of some form on other planets in the unirverse? ” Of the 535 individuals surveyed, 326 responded “Yes”. When the same question was asked on September 3-5, 1996, 385 of the 535 individuals surveyed responded “Yes”. Test the claim that the proportion of adults who believe that there is life on other planets has decreased since September 3-5, 1996. Chapter 10 – Matched pairs For each of the following a. State the null and alternate hypotheses. b. In words, define the random variable. c.

State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. 1. A professor measured the time (in seconds) required to catch a falling meter stick for 12 randomly selected students’ dominant and nondominant hand. The professor claims that the reaction time of an individual’s dominant hand is less that the reaction time of their nondominant hand. The data obtained are below. StudentDominnantNondominant 10. 1770. 179 20. 2100. 202 30. 1860. 208 40. 1890. 187 50. 1980. 215 60. 1940. 193 70. 1600. 194 80. 1630. 160 90. 1660. 209 00. 1520. 164 110. 1900. 210 120. 1720. 197 2. A physical therapist wishes to determine whether an exercise program increase flexibility. He measures the flexibility (in inches) of 12 randomly selected subjects both before and after an intensive eight-week training program and obtains the following data. Test the claim that the flexibility before the exercise program is less than the flexibility after the exercise program. SubjectBeforeAfter 118. 519. 25 221. 521. 75 316. 516. 5 42120. 5 52022. 25 61516 719. 7519. 5 815. 7517 91819. 25 102219. 5 111516. 5 1220. 520 Chapter 11 – Goodness of Fit For each of the following. a.

State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. d. Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. h. State the Type I error 1. A USA Today Snapshot states that 53% of adult shoppers prefer to pay cash for purchases, 30% use checks, 16% use credit cards and 1% have no preference. The owner of a large store randomly selected 800 shoppers and asked their payment preference. The results were that 400 paid cash, 210 paid by check, 170 paid with a credit card and 20 had no preference.

At ? = 0. 01, test the claim that the owner’s customers have the same preference as those surveyed. 2. An obstetrician wants to know whether the proportion of children born each day of the week is the same. She randomly selects 500 birth records and obtains the data that 57 children were born on Sunday, 78 on Monday, 74 on Tuesday, 76 on Wednesday, 71 on Thursday, 81 on Friday and 63 on Saturday. Test the obstetricians claim. Chapter 11 – Test of Independence For each of the following. a. State the null and alternate hypotheses. b. In words, define the random variable. c. State the distribution for the test. . Sketch a picture of the situation. e. Calculate the p-value. f. State your decision. g. Write an appropriate conclusion. h. State the Type II error 1. Consider the following table of Level of Education versus marital status from the US. Census Bureau. Marital StatusDid not graduate high schoolHigh School graduateSome CollegeCollege GraduateTOTAL Never married4012779065657685 Married, Spouse present15122360762700329811 Married, Spouse absent1877200614351489 Separated109415151214598 Widowed5000475722641456 Divorced2951704756493766 TOTAL f. Are marital status and level of education independent?

Conduct a hypothesis test at a level of significance of 5%. 2. Consider the following table which represents the size of a farm and the tenure of the operator (a full owner owns all the acreage farmed, a part owner owns some of the land and rents the rest, a tenant leases the land farmed). (from Statistical Abstract of the US, 2000) Size of farmFull ownerPart ownerTenantTOTAL Under 50 acres4605748 50-179 acres40913153 180-499 acres18916945 500-999 acres5010323 > 1000 acres4011422 TOTAL g. Are size of farm and tenure of operator independent? Conduct a hypothesis test at a level of significance of 3%.

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