Respuesta :
Answer:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
Step-by-step explanation:
Information given
[tex]\bar X=4600[/tex] represent the sample mean for the amount spent on medicines
[tex]\mu[/tex] population mean
s=800 represent the sample standard deviation
n=1800 represent the sample size
Solution
The confidence interval for the true population mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We can calculate the degrees of freedom with:
[tex]df=n-1=1800-1=1799[/tex]
We know that the Confidence level is 0.90 or 90%, the value of significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,1799)".And we see that [tex]t_{\alpha/2}=1.646[/tex]
Replcing in the formula for the confidence interval we got:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
