"dataset_name": "high_school_statistics"
"description": "The following are multiple choice questions (with answers) about high\
  \ school statistics.\n\nQ: A new smartwatch is manufactured in one part of a factory,\
  \ then secured for shipping in another, independent part of the factory. The weight\
  \ of the smartwatch has a mean of 62 grams and a standard deviation of 1.0 grams.\
  \ The weight of the packaging (box, user's guide, bubble wrap, etc.) has a mean\
  \ of 456 grams and a standard deviation of 6 grams. Together, the distribution of\
  \ the weight of the smartwatch and its packaging would have the following mean and\
  \ standard deviation:\n(A) Mean 518 grams; standard deviation 7.0 grams (B) Mean\
  \ 518 grams; standard deviation 3.5 grams (C) Mean 518 grams; standard deviation\
  \ 6.1 grams (D) Mean 394 grams; standard deviation 6.1 grams\nA: Let's think step\
  \ by step. Since the weight of the watch and the weight of the packaging are independent\
  \ random variables, the mean and variance of their sum is equal to the sum of their\
  \ individual means and variances. So the mean is 62 + 456 = 518 grams, and the variances\
  \ is 1.0^2 + 6.0^2 = 37, leading to a standard deviation of 6.1 grams. The answer\
  \ is (C).\n\nQ: After a frost warning was issued, the owner of a large orange grove\
  \ asked his workers to spray all his trees with water. The water was supposed to\
  \ freeze and form a protective covering of ice around the orange blossom. Nevertheless,\
  \ the owner suspected that some trees suffered considerable damage due to the frost.\
  \ To estimate the proportion of trees that suffered more than 50 percent damage\
  \ due to the frost, he took a random sample of 100 trees from his grove. What is\
  \ the response variable in this experiment?\n(A) The proportion of trees that suffered\
  \ more than 50 percent damage due to frost. (B) The number of trees affected by\
  \ the frost. (C) The number of trees sampled from the grove. (D) For each sampled\
  \ tree, whether it suffered more than 50 percent damage or at most 50 percent damage.\n\
  A: Let's think step by step. In this experiment, the response variable is what is\
  \ measured. For each tree, what is measured is whether or not it suffered more than\
  \ 50 percent damage due to the frost. The answer is (D).\n\nQ: Suppose X and Y are\
  \ random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and var(Y) = 12. What\
  \ are the expected value and variance of the random variable X + Y?\n(A) E(X + Y)\
  \ = 99, var(X + Y) = 8.5 (B) E(X + Y) = 99, var(X + Y) = 13 (C) E(X + Y) = 99, var(X\
  \ + Y) = 17 (D) There is insufficient information to answer this question.\nA: Let's\
  \ think step by step. While means of sums of random variables add (regardless of\
  \ whether the variables are independent) in order to determine the variance of a\
  \ sum of random variables, we need to know not just their individual variances but\
  \ the covariance of the two variables, which is not given in this problem. The answer\
  \ is (D).\n\nQ: Which of the following sets has the smallest standard deviation?\
  \ Which has the largest?\nI: {1,2,3}\nII: {-10,10}\nIII: {100}\n(A) I, II (B) II,\
  \ III (C) III, I (D) III, II\nA: Let's think step by step. The variance of distribution\
  \ I is the expected squared deviation from its mean (which is 2), so the variance\
  \ is 2/3 . The variance of distribution II is 10^2 (because both elements are 10\
  \ away from the mean of zero). The variance of distribution III is 0, since it has\
  \ a single entry. So distribution III has the smallest standard deviation and distribution\
  \ II has the largest. The answer is (D).\n\nQ: Which of the following is a correct\
  \ statement about correlation?\n(A) If the slope of the regression line is exactly\
  \ 1, then the correlation is exactly 1. (B) If the correlation is 0, then the slope\
  \ of the regression line is undefined. (C) Switching which variable is called x\
  \ and which is called y changes the sign of the correlation. (D) The correlation\
  \ r is equal to the slope of the regression line when z-scores for the y-variable\
  \ are plotted against z-scores for the x-variable.\nA: Let's think step by step.\
  \ Statement A is false because the slope of the regression line being exactly 1\
  \ can occur even when the two variables are not perfectly correlated. Statement\
  \ B is false because uncorrelated variables regression lines can have slope zero.\
  \ Statement C is false because correlation is symmetric in the two random variables.\
  \ The answer is (D).\n\n"
"group": "mmlu_flan_cot_fewshot_stem"
"include": "_mmlu_flan_cot_fewshot_template_yaml"
"task": "mmlu_flan_cot_fewshot_high_school_statistics"
