Final answer:
The question involves calculating and interpreting sample mean, standard deviation, and z scores in different contexts, using these statistical measures to analyze and infer about broader populations or distributions.
Step-by-step explanation:
The question pertains to the calculation and interpretation of statistical measures such as the sample mean and sample standard deviation, as well as the understanding of the suitability of statistical techniques for analyzing data. A researcher studying soda sugar content or statistics exam scores must use the mean and standard deviation to summarize data and infer about the population from the sample. Making assumptions about the normal distribution of data plays a key role in choosing the correct hypothesis test or describing an individual score in relation to the distribution.
For instance, if a population mean is 13, and you have a sample mean of 12.8 with a standard deviation of 2, knowing the sample size is 20 permits application of specific distributions to conduct hypothesis testing, assuming a normal population distribution. Additionally, calculating a z score for an exam score in a biology class with a known mean and standard deviation allows us to interpret how far or how many standard deviations a score is from the mean.