We assume that the data are from a simple random sample, and that the population follows a normal distribution. Because low scores should indicate a Mexican cultural orientation, these results helped to establish the validity of the test. The assumptions required are that the data are a simple random sample from a normally distributed population. The detector readings were as follows. The distribution is somewhat skewed to the right, but not strongly enough to forbid use of the t procedures.
Manufacturers also wish to be able to make claims about the variability of the radon detectors.
Gas chromatography is a sensitive technique used by chemists to measure small amounts of compounds. The response of a gas chromatograph is calibrated by repeatedly testing specimens containing a known amount of the compound to be measured. Then explain to a chemist who knows no statistics what your margin of error means. The standard error is a measure of the sampling error, or variability in means from sample to sample. When the underlying data are normally distributed, then we know the distribution of sample mean, can assign a probability, or confidence level to a margin of error by taking the appropriate multiple of the standard error.