Respuesta :
Answer:
C) (-5%.15%)
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X =10\%=0.1 [/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma[/tex]=5% =0.05 represent the population standard deviation
2) Confidence interval
We assume that the random variable X who represent The Ishares Bond Index fund (TLT) follows this distribution:
[tex]X \sim N(\mu, \sigma=10\%=0.1)[/tex]
The confidence interval for the returns on TLT is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\sigma[/tex] (1)
In order to calculate the critical value [tex]z_{\alpha/2}[/tex]. Since the Confidence is 0.66 or 66%, the value of [tex]\alpha=0.34[/tex] and [tex]\alpha/2 =0.17[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.17,0,1)".And we see that [tex]z_{\alpha/2}=0.95[/tex]
Now we have everything in order to replace into formula (1):
[tex]0.05-0.95(0.1)=-0.05[/tex]
[tex]0.05+0.95(0.1)=0.15[/tex]
So on this case the 66% confidence interval would be given by (-0.05;0.15) and we can convert this into % and wr got (-5%; 15%).
