Exam 2: Data

Associations For each pair of variables, indicate what association you expect: positive(+), negative(-), curved(C), or none(N). _ a. the number of miles a student lives from school; the student's grade point average b. a person's blood alcohol level; time it takes the person to solve a maze c. weekly sales of hot chocolate at a Montana diner; the number of auto accidents that week in that town d. The price charged for fund-raising candy bars; number of candy bars sold e. the amount of rainfall during growing season; the crop yield (bushels per acre)

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches. Their model is $\hat{\text{cheerios}}$ = 0.56 + 5.11(diameter). -If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will Increase by about……

One of your classmates is reading through the program for Friday night's football game.Among other things, the program lists the players' positions and their weights. Yourclassmate comments, "There is a strong correlation between a player''s position and their weight." a. Explain why your classmate's statement is in error. b. What other variable might be listed in the program that could be used to correctlyidentify a correlation with weight?

After conducting a marketing study to see what consumers thought about a new tinted contact lens they were developing, an eyewear company reported, "Consumer satisfaction is strongly correlated with eye color." Comment on this observation.

A study examined the number of trees in a variety of orange groves and the corresponding number of oranges that each grove produces in a given harvest year. Linear regression was calculated and the results are below. linear regression results: Dependent Variable: oranges Independent Variable: trees Sample size: 9 R-sq = 0.886 s = 31394.7 Parameter Estimate Std. Err. Constant 390.59 16328.8 Trees 525.84 71.22 -Does the value of s concern you? How might you deal with this data differently to address this problem?

A lakeside restaurant found the correlation between the daily temperature and the number of meals they served to be 0.40. On a day when the temperature is two standard deviations above the mean, the number of meals they should plan on serving is __________the mean.

During a science lab, students heated water, allowed it to cool, and recorded the temperature over time. They computed the difference between the water temperature and the room temperature. The results are in the table. Time (in minutes) 10 20 30 40 50 60 Difference in temp. (degrees F) 68 36 20 10 6 4 -Use the equation to predict the difference in temperature at time 0 minutes. What does this value represent?

Residuals are...

Current research states that a good diet should contain 20-35 grams of dietary fiber. Research also states that each day should start with a healthy breakfast. The nutritional information for 77 breakfast cereals was reviewed to find the grams of fiber and the number of calories per serving. The scatterplot below shows the relationship between fiber and calories for the cereals. -Do you think a model could accurately predict the number of calories in a serving of cereal that has 22 grams of fiber? Explain.

A school board study found a moderately strong negative association between the number of hours high school seniors worked at part-time jobs after school hours and the students' grade point averages. a. Explain in this context what "negative association" means. b. Hoping to improve student performance, the school board passed a resolution urging parents to limit the number of hours students be allowed to work. Do you agree or disagree with the school board's reasoning? Explain.

Mistakes. Describe the mistake made in the following analyses: a. Ten teachers compute their average test scores for all their students. Then the superintendent collects their data and finds the school average. He repeats this process for eight different schools and finds a positive correlation between the age of the school average age of the teachers at a school and their average score. b. The mayor of a city is concerned that the population of the city is growing faster than revenue. He calculates that over the last 5 years, the year and the size of the city have a R-sq of 95.7%. With such a high value, the may or confidently predicts the population for the next three years of fiscal planning.

A researcher notes that there is a positive correlation between the temperature on a summer day and the number of bees that he can count in his garden over a 5-minute time span. a. Describe what the researcher means by a positive correlation. b. If the researcher calculates the correlation coefficient using degrees Fahrenheit instead of Celsius, will the value be different?

A correlation of zero between two quantitative variables means that

If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)?

Variables X and Y have r = 0.40. If we decrease each X value by 0.1, double each Y value, and then interchange them (put X on the Y- axis and vice versa) the new correlation will be

Over the past decade a farmer has been able to increase his wheat production by about the same number of bushels each year. His most useful predictive model is probably…

The relationship between the number of hours a person practices a task and the time it takes them to complete the task is calculated to have R-sq = 56.7%. The value of the correlation coefficient is

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004: 2004 US\ Carat 494.82 0.12 768.03 0.17 1105.03 0.20 1508.88 0.25 1826.18 0.28 2096.89 0.33 2004 US \ Carat 688.24 0.15 944.90 0.18 1071.75 0.21 1504.44 0.26 1908.28 0.29 2409.76 0.35 2004 US \ Carat 748.10 0.16 1076.18 0.19 1289.20 0.23 1597.63 0.27 2038.09 0.32 -Do you think a linear model is appropriate here? Explain.

Baseball coaches use a radar gun to measure the speed of pitcher’s fastball. They also record outcomes such as hits and strikeouts. The scatterplot below shows the relationship between the average speed of a fastball and the average number of strikeouts per nine innings for each pitcher on the Bulldogs, based on the past season. -Do you think there is a pattern? Describe the association between speed and the number of strikeouts.

Math and Verbal Suppose the correlation between SAT Verbal scores and Math scores is0.57 and that these scores are normally distributed. If a student's Verbal score places her atthe 90th percentile, at what percentile would you predict her Math score to be? (Show your work.)