Introduction to Statistics Exam 1 Practice Problems
Math 203, Central College, Spring 2000
Tom Linton
  1. You are designing a study to investigate relationships between persons (their lifestyles, habits and physical characteristics) and problems with vision. A key seems to be "exposure to sunshine".
    1. Give an example of both a categorical and quantitative variable which you would analyze for each individual (patient) you study.
    2. Other studies suggest that wearing a hat (often) lowers the risk of a common eye problem (cataracts, which is roughly spots of opaqueness, or non-see-throughness in the eyes). You decide to ask patients in your study what percentage of the time they wore a hat when they were outside in sunshine, and measure the percentage of their eyes which suffer from cataracts.
      1. Which variable (time with hat on, or percentage of cataracts in the eye) is the response variable?
      2. Do the other studies suggest a positive or negative association between the explanatory and response variable?
      3. Upon analysis of the data on how often patients wore a hat, when outside in sunshine, you see a distribution which is quite skewed to the right. Draw a possible density function of this distribution and indicate the mean and median of your data-plot. In particular, which is larger, the mean or the median?
  2. Corn is an important food source for chickens, but normal corn lacks certain amino acids (protein building blocks) which is believed to limit the potential growth of baby chicks. Scientists working for Colonel Sanders have developed a new strain of corn believed to supply chicks with more of these amino acids. To test this new strain of corn, two groups (with 20 chicks each) of one-day-old chicks were fed equal rations of the two varieties of corn (one group got normal corn, the other received the new strain of corn). Here are the weights (in grams) of the normal corn group after 21 days.
    3. Normal Corn Chick Weights
    380 321 366 356
    283 349 402 462
    356 410 329 399
    350 380 316 272
    345 455 360 431
    1. Calculate the mean, x-bar, and standard deviation Sx, for the normal corn group of chickens.
    2. Calculate the 5 number summary (min, Q1, median, Q3, and max) for the group of chickens which were fed normal corn.
    3. A boxplot summarizing the results for the group of chickens which were fed the new strain of corn is shown below. From the boxplot, estimate values for the 5 number summary for the new corn group of chickens.


    4. Add a boxplot for the group of chickens which were fed normal corn under the boxplot for the group fed the new strain of corn. Based on the boxplots, which data set (normal corn or new corn) is more spread out?
    5. The group fed the new strain of corn had a mean weight of 402.95 grams (after 21 days) with a standard deviation of 42.73 grams. What do these data and the 5 number summaries show about the effects of the new strain of corn?
  3. Chickens at Colonel Sanders egg farm lay eggs whose weights are distributed in an approximately normal fashion. The mean weight is 1.54 ounces with a standard deviation of 0.23 ounces.
    1. The interval from m - s to m + s contains roughly what percentage of the eggs laid?
    2. Which interval, centered at m, contains about 95% of the eggs' weights  (give values for a and b so that eggs with weights from a to b constitute about 95% of all egg weights)?
    3. Eggs weighing more than 1.9 ounces are sold as extra large eggs. Out of 2000 eggs collected at the Sanders farm, how many would you expect to be extra large?
    4. How much would an egg weigh if it was heavier than 23% of all eggs laid at the Colonel's farm?
  4. The game of golf is one where a low score is better than a high score, so as you get better, your score decreases. A golf instructor believes that more experience playing the game improves your score. To investigate this claim, she collects data from 10 of her students, namely the number of years each student has been playing golf, and the average score of each student.
    1. Which variable (years playing golf or average score) is the response variable and which is the explanatory variable?
    2. According to this golf instructor, would you expect a positive or negative association between these two variables? Explain.
    3. If the least squares regression line equation for the instructor's 10 data points was Y = 130 - 12.8*X, what is the meaning (in common-everyday language) of the slope -12.8?
  5. Tom's parents are concerned that he seems short for his age. Their doctor has the following record of Tom's height:
    6. X = Age in months 28 34 36 37 40
    Y = Height in inches 51 54 55 56 57
    1. Make a scatterplot of these data.
    2. Find the equation of the least-squares regression line, and the correlation r.
    3. Predict Tom's height at an age of 30 months.