Respuesta :
Answer:
The 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
The data provided is:
S = {112, 120, 98, 55, 71, 35, 99, 142, 64, 150, 150, 55, 100, 132, 20, 70, 93}
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{17}\times[112+120+98+...+93]=92.1176\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 25041.7647}=39.56[/tex]
The critical value of t for 95% confidence level and n - 1 = 16 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 16}=2.120[/tex]
*Use a t-table.
Compute the 95% confidence interval for the hemoglobin reading for all the patients in the hospital as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=92.1176\pm 2.120\times\frac{39.56}{\sqrt{17}}\\\\=92.1176\pm 20.3408\\\\=(71.7768, 112.4584)\\\\\approx (72, 112)[/tex]
Thus, the 95% confidence interval for the hemoglobin reading for all the patients in the hospital is (72, 112).
