Respuesta :
The 95% confidence interval for the true population mean based on a sample is (222.52, 227.48)
We know that, the confidence interval is:
[tex]\bar{x}\pm z\frac{\sigma}{\sqrt{n} }[/tex]
where,
[tex]\bar{x}[/tex] is the sample mean.
z is the critical value.
n is the sample size.
σ (OR s) is the standard deviation for the population.
In this question, we need to calculate the 95% confidence interval for the true population mean based on a sample.
So, [tex]\alpha=0.95[/tex]
z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} =0.975[/tex] , so the critical value is z = 1.96
We have been given x¯=225, s = 8.5, and n = 45.
[tex]\Rightarrow \bar{x}+ z\frac{s}{\sqrt{n} }\\\\ = 225+1.96\frac{8.5}{\sqrt{45} }\\\\=227.48[/tex]
And,
[tex]\Rightarrow \bar{x}- z\frac{s}{\sqrt{n} }\\\\ = 225-1.96\frac{8.5}{\sqrt{45} }\\\\=222.52[/tex]
Therefore, the 95% confidence interval for the true population mean based on a sample is (222.52, 227.48)
Learn more about the confidence interval here:
https://brainly.com/question/28064687
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