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

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)(s)/(√(n))\\\\\Rightarrow\ E=(1.745884)(3)/(√(17))\\\\\Rightarrow\ E=01.27031720154\approx1.2703`

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