Respuesta :
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, [tex]H_0[/tex] : [tex]\mu[/tex] = 15
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 15
The test statistics that is used here is One sample t-test statistics;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean
[tex]\mu[/tex] = population mean = 15
s = sample standard deviation = 2.4
n = sample size = 23
So, test statistics = [tex]\frac{\bar X-15}{\frac{2.4}{\sqrt{23} } }[/tex] ~ [tex]t_2_2[/tex]
2.24 = [tex]\frac{\bar X-15}{\frac{2.4}{\sqrt{23} } }[/tex]
[tex]2.24 \times {\frac{2.4}{\sqrt{23} } } = \bar X - 15[/tex]
1.21 = [tex]\bar X[/tex] - 15
[tex]\bar X[/tex] = 1.21 + 15 = 16.21
Therefore, mean of n = 23 observations is 16.21 .
