The one‑sample t t statistic from a sample of n = 23 n=23 observations for the two‑sided test of H 0 : μ = 15 H0:μ=15 versus H α : μ > 15 Hα:μ>15 has the value t = 2.24 t=2.24 . If the standard deviation from the sample is 2.4, what is the mean of these n = 23 n=23 observations?

Mean of these n = 23 observations is 16.21 .

Step-by-step explanation:

We are given with the one‑sample t statistic from a sample of n = 23 observations for the two‑sided test of H0 : μ = 15 versus Hα : μ > 15 has the value t = 2.24 . Also, the standard deviation from the sample is 2.4.

So, Null Hypothesis, : = 15

Alternate Hypothesis, : > 15

The test statistics that is used here is One sample t-test statistics;

             T.S. = ~

where, = sample mean

            = population mean = 15

            s = sample standard deviation = 2.4

            n = sample size = 23

So, test statistics = ~

                  2.24  =  

              1.21 = - 15

                  = 1.21 + 15 = 16.21      

Therefore, mean of n = 23 observations is 16.21 .