Question

The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 3 inches and an unknown population mean. If a random sample of 17 dogs is taken and results in a sample mean of 28 inches, find the error bound (EBM) of the confidence interval with a 90% confidence level.

Answer 1

Answer: 1.2703

Step-by-step explanation:

Given : Sample size : n= 17, which is a small sample (n<30), so we use t-test.

Significance level : $\alpha:1-0.90=0.1$

Then , Critical value : $t_{n-1,\alpha/2}=t_{16, 0.05}\pm1.745884$

Standard deviation: $s=3\text{ inches}$

The formula to find the margin of error : -

$E=t_{n-1,\alpha/2}\dfrac{s}{\sqrt{n}}\\\\\Rightarrow\ E=(1.745884)\dfrac{3}{\sqrt{17}}\\\\\Rightarrow\ E=01.27031720154\approx1.2703$

Hence, the error bound (EBM) of the confidence interval with a 90% confidence level.=1.2703