dataset_name: high_school_statistics
description: The following are multiple choice questions (with answers) about high
  school statistics.
fewshot_config:
  sampler: first_n
  samples:
  - question: '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:

      (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'
    target: 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).
  - question: '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?

      (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.'
    target: 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).
  - question: '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?

      (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.'
    target: 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).
  - question: 'Which of the following sets has the smallest standard deviation? Which
      has the largest?

      I: {1,2,3}

      II: {-10,10}

      III: {100}

      (A) I, II (B) II, III (C) III, I (D) III, II'
    target: 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).
  - question: 'Which of the following is a correct statement about correlation?

      (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.'
    target: '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).'
group: mmlu_flan_cot_fewshot_stem
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_high_school_statistics
