Question

The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 6 inches and an unknown population mean. If a random sample of 18 snakes is taken and results in a sample mean of 61 inches, find the margin of error (ME) of the confidence interval with a 90% confidence level. Round your answer to three decimal places.

Answer 1

Answer: 2.460

Step-by-step explanation:

The formula of Margin of Error for (n<30):-

$ME=t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 18

Level of confidence = 0.90

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

Using the t-distribution table ,

Critical value : $t_{n-1, \alpha/2}=t_{17,0.05}= 1.7396$

Standard deviation: $\sigma=\text{ 6 inches }$

Then, we have

$ME=( 1.7396)\dfrac{6}{\sqrt{18}}\approx2.460$

Hence, the margin of error (ME) of the confidence interval with a 90% confidence level = 2.460