Question

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?

Answer 1

Answer:

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, $H_0$ : $\mu$ = 15

Alternate Hypothesis, $H_1$ : $\mu$ > 15

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

             T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean

            $\mu$ = population mean = 15

            s = sample standard deviation = 2.4

            n = sample size = 23

So, test statistics = $\frac{\bar X-15}{\frac{2.4}{\sqrt{23} } }$ ~ $t_2_2$

                  2.24  =  $\frac{\bar X-15}{\frac{2.4}{\sqrt{23} } }$

              $2.24 \times {\frac{2.4}{\sqrt{23} } } = \bar X - 15$  

              1.21 = $\bar X$ - 15

                 $\bar X$ = 1.21 + 15 = 16.21      

Therefore, mean of n = 23 observations is 16.21 .