One- and two-sample t tests.

The R function t.test() can be used to perform both one and two sample t-tests on vectors of data. The function contains a variety of options and can be called as follows: > t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95) Here x is a numeric vector of data values and y is an optional numeric vector of data values. If y is excluded, the function performs a one-sample t-test on the data contained in x, if it is included it performs a two-sample t-tests using both x and y. The option mu provides a number indicating the true value of the mean (or difference in means if you are performing a two sample test) under the null hypothesis. The option alternative is a character string specifying the alternative hypothesis, and must be one of the following: "two.sided" (which is the default), "greater" or "less" depending on whether the alternative hypothesis is that the mean is different than, greater than or less than mu, respectively. For example the following call: > t.test(x, alternative = "less", mu = 10) performs a one sample t-test on the data contained in x where the null hypothesis is that =10 and the alternative is that <10. The option paired indicates whether or not you want a paired t-test (TRUE = yes and FALSE = no). If you leave this option out it defaults to FALSE. The option var.equal is a logical variable indicating whether or not to assume the two variances as being equal when performing a two-sample t-test. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used. If you leave this option out it defaults to FALSE. Finally, the option conf.level determines the confidence level of the reported confidence interval for in the one-sample case and 1-2 in the two-sample case. A. One-sample t-tests Ex. An outbreak of Salmonella-related illness was attributed to ice cream produced at a certain factory. Scientists measured the level of Salmonella in 9 randomly sampled batches of ice cream. The levels (in MPN/g) were: