Question: Identify the assumptions for the onesample t test; compute a one-sample t test and interpret the results.
• We compute a one-sample t test to compare a mean value measured in a sample to a known value in the population_ It is specifically used to test hypotheses concerning a single population mean from a population with an unknown variance_ We make three assumptions for this test: normality, random sampling, and independence.
• The larger the value of the test statistic, the less likely a sample mean would be to occur if the null hypothesis were true, and the more likely we are to reject the null hypothesis. The test statistic for a one-sample t test is the difference between the sample mean and population mean, divided by the estimated standard error:
tobt = M - μ, where sM = SD
sM √n
• The estimated standard error is an estimate of the standard deviation of a sampling distribution of sample means. It is an estimate of the standard error or standard distance that sample means can be expected to deviate from the value of the population mean stated in the null hypothesis.