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MATH 225N WEEK 8 DATA INTERPRETATION
LINEAR REGRESSION ASSIGNMENT FULL
SOLUTION 2026
◉ A scientist was studying the effects of a new fertilizer on crop yield. She randomly assigned half of the plots on a farm to group one and the remaining plots to group two. On the plots in group one, the new fertilizer was used for a year. On the plots in group two, the old fertilizer was used. At the end of the year the average crop yield for the plots in group one was compared with the average crop yield for the plots in group two.. Answer: experiment ◉ Identify the type of sampling used. A travel industry researcher interviews all of the passengers on five randomly selected cruises. What sampling technique is used?. Answer: cluster ◉ Identify the type of sampling used. A lobbyist for the oil industry assigns a number to each senator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the senators corresponding to these numbers. What sampling technique was used?. Answer: simple random
◉ Determine what type of observational study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.. Answer: cross- sectional; Information is collected at a specific point in time. ◉ Identify the type of sampling used. Thirty-five math majors, 47 music majors and 51 history majors are randomly selected from 376 math majors, 591 music majors and 267 history majors at the state university. What sampling technique is used?. Answer: stratified ◉ Determine what type of observational study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative
Find the IQR.. Answer: 227 ◉ Provide an appropriate response. Over the last 10 years four mutual funds all had the same mean rate of return, 12%. These mutual funds had different standard deviations as follows: Mutual Money 8%, Co-joined Investments 6%, Together Fund 4%, All for One Fund 9%. Which mutual fund investment is the most consistent in rate of return?. Answer: Together Fund ◉ Provide an appropriate response. Last year batting averages in professional baseball averaged 0.256 with a high of and a low of (minimum 250 at-bats). Based on this information, which measure of variation could be calculated?. Answer: range ◉ Provide an appropriate response. Given the following five-number summary, find the IQR. 2.9, 5.7, 10.0, 13.2, 21.1.. Answer: 7. ◉ Which measure of central tendency may not exist for all numeric data sets?. Answer: mode
◉ Provide an appropriate response. Civil engineers often use the straight-line equation, E(y) = β0 + β1x, to model the relationship between the mean shear strength E(y) of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 triplet tests is shown in the accompanying table followed by a SAS printout of the regression analysis. For this data set, R2 = .9052. Give a practical interpretation of R2, the coefficient of determination for the least squares model. Express R2 to the nearest whole percent.. Answer: About 91% of the total variation in the sample of y-values can be explained by (or attributed to) the linear relationship between shear strength and precompression stress. ◉ A traffic officer is compiling information about the relationship between the hour or the day and the speed over the limit at which the motorist is ticketed. He computes a correlation coefficient of 0.12. What does this tell the officer?. Answer: There is a weak positive linear correlation.
For this data set, R2 = .9052. Give a practical interpretation of R2, the coefficient of determination for the least squares model. Express R2 to the nearest whole percent.. Answer: About 91% of the total variation in the sample of y-values can be explained by (or attributed to) the linear relationship between shear strength and precompression stress. ◉ Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools." An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Total GMAT scores range from 200 to 800. A simple linear regression of SALARY versus GMAT using 25 data points yields the regression equation given below: y = 228x - 92, Give an interpretation of the y-intercept.. Answer: The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data. ◉ Find the indicated probability. If necessary, round to three decimal places.
Suppose that E and F are two events and that N(E and F) = 450 and N(E) = 870. What is P(E)?. Answer: 0. ◉ In a contest in which 7 contestants are entered, in how many ways can the 4 distinct prizes be awarded?. Answer: 840 ◉ Solve the problem. In the game of craps two dice are rolled and the up faces are totaled. If the person rolling the dice on the first roll rolls a 7 or an 11 total they win. If they roll a 2, 3, or 12 on the first roll they lose. If they roll any other total then on subsequent rolls they must roll that total before rolling a 7 to win. What is the probability of winning on the first roll?. Answer: 0. ◉ Suppose a basketball player is an excellent free throw shooter and makes 91% of his free throws (i.e., he has a 91% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot four free throws. Find the probability that he misses all four consecutive free throws. Round to the nearest ten-thousandth.. Answer: 0. ◉ Provide an appropriate response.
◉ Provide an appropriate response. The produce manager at a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x apples. Determine the mean number of oranges purchased by a customer.. Answer: 3. ◉ Provide an appropriate response. The sum of the probabilities of a discrete probability distribution must be. Answer: equal to one ◉ A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.). Answer: $637.
◉ Consider the discrete probability distribution to the right when answering the following question. Find the probability that x exceeds 4.. Answer: 0. ◉ Consider the discrete probability distribution to the right when answering the following question. Find the probability that x equals 4.. Answer: 0. ◉ A random variable is. Answer: a numerical measure of the outcome of a probability experiment. ◉ Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(57 < X < 105).. Answer: 0. ◉ The amount of corn chips dispensed into a 32-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 32.5 ounces and a standard deviation of 0. ounce. What chip amount represents the 67th percentile for the bag weight distribution? Round to the nearest hundredth.. Answer: 32. ◉ Furnace repair bills are normally distributed with a mean of 269 dollars and a standard deviation of 30 dollars. If 144 of these repair bills are randomly selected, find the probability that they have a mean cost between 269 dollars and 271 dollars.. Answer: 0.
Find the z-score for which the area under the standard normal curve to its left is 0.96. Answer: 1. ◉ A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6%? A previous study indicates that the proportion of households with two computers is 23%.. Answer: 268 ◉ The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume σ = 14 minutes.. Answer: 11 ◉ In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $109.33 per class. Assuming the population standard deviation of the amount spent per owner is $12, construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class.. Answer: ($106.29, $112.37); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.29 and $112.37. ◉ When 455 junior college students were surveyed,105 said that they have previously owned a motorcycle. Find a point estimate for p, the
population proportion of students who have previously owned a motorcycle.. Answer: 0. ◉ Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were obtained:. Answer: (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and 107.1 beats per minute. ◉ Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were obtained:. Answer: (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and 107.1 beats per minute. ◉ A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658
◉ Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.. Answer: (0.5496, 0.5754) ◉ Mamma Temte bakes six pies a day that cost $2 each to produce. On 25% of the days she sells only two pies. On 14% of the days, she sells 4 pies, and on the remaining 61% of the days, she sells all six pies. If Mama Temte sells her pies for $5 each, what is her expected profit for a day's worth of pies? [Assume that any leftover pies are given away and therefore are counted as a loss.]. Answer: $11. ◉ Find the area under the standard normal curve between z = 1.5 and z = 2.5.. Answer: 0. ◉ A recent study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Thirty-two hundred Florida residents were surveyed. Which of the following is the population used in the study?. Answer: all Florida residents ◉ Find the area under the standard normal curve to the left of z = 1.25.. Answer: 0.
◉ In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation, σ, is 2.4. Compute the 95% confidence interval for μ.. Answer: (61.9, 64.9) ◉ Identify the type of sampling used. A writer for an art magazine randomly selects and interviews fifty male and fifty female artists. What sampling technique is used?. Answer: stratified ◉ Provide an appropriate response. The percentage of measurements that are above the 63rd percentile is. Answer: 37% ◉ Provide an appropriate response. The cell phone conversations of a random sample of 120 students has a standard deviation of 9.7 minutes. Find the margin of error, E, using a 98% confidence interval.. Answer: 2. ◉ Provide an appropriate response.
customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the pet store.. Answer: number of items - discrete; total time - continuous ◉ A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 40 minutes. The owner has randomly selected 22 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 40 minutes. Suppose the P- value for the test was found to be 0.0281. State the correct conclusion.. Answer: At α = 0.025, we fail to reject H0. ◉ The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a particular tire of this brand will last longer than 57,100 miles?. Answer: 0. ◉ A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 312 seconds.. Answer: 0. ◉ Identify the type of sampling used.
Every fifth adult entering an airport is checked for extra security screening. What sampling technique is used?. Answer: systematic ◉ Identify the type of sampling used. At a local technical school, five auto repair classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used?. Answer: cluster ◉ Determine the level of measurement of the variable. the year of manufacture of a car. Answer: interval ◉ Identify the type of sampling used. A travel industry researcher interviews all of the passengers on five randomly selected cruises. What sampling technique is used?. Answer: cluster ◉ Identify the type of sampling used. A lobbyist for the oil industry assigns a number to each senator and then uses a computer to randomly generate ten numbers. The lobbyist
