1. (1) The normal distribution content standards for high school are to:

   1. (a) determine if a data set is normally distributed;
   2. (b) use technology to find the mean and standard deviation of a normally distributed data set and apply the empirical rule to estimate population percentages; and
   3. (c) estimate areas under a normal curve to solve problems in context, using calculators, spreadsheets, and tables as appropriate.

2. (2) The experimental design content standards for high school are to:

   1. (a) describe the purposes of and differences among sample surveys, experiments, and observational studies and explain how randomization relates to each;

   2. (b) describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect by:

      1. (i) explaining the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments; and
      2. (ii) evaluating where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest;

   3. (c) evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by:

      1. (i) simulating a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability; and
      2. (ii) demonstrating that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.

3. (3) The statistical inference using simulation content standards for high school are to:

   1. (a) distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population;

   2. (b) estimate a population parameter from a representative sample by:

      1. (i) understanding why the sample statistic is the best estimate for the associated population parameter;

      2. (ii) understanding that sampling variability introduces uncertainty in the estimate, and account for the uncertainty with a confidence interval by:

         1. (A) using resampling with replacement from an observed sample to produce a sampling distribution;
         2. (B) verifying that a sampling distribution is centered at the population mean and approximately normal if the sample size is large enough;
         3. (C) verifying that 95% of sample means are within two standard deviations of the sampling distribution from the population mean; and
         4. (D) creating and interpreting a 95% confidence interval based on an observed mean from a sampling distribution;

   3. (c) use data from a randomized experiment to test the hypothesis that two groups are equal by:

      1. (i) interpreting the difference or ratio between the group means as the observed effect between the groups; and
      2. (ii) understanding that an observed effect may be due to randomization and using a randomization test (repeatedly reshuffling the observed data into new groups) to determine the probability that an observed effect is due to randomization alone.

Authorizing statute(s): Mont. Const. Art. X, sec. 9, 20-2-114, 20-7-101, MCA

Implementing statute(s): Mont. Const. Art. X, sec. 9, 20-2-121, 20-3-106, 20-7-101, MCA

History: NEW, 2025 MAR, 10-53-141, Eff. 7/1/26.