Question

In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $109.33 per class. Assuming the population standard deviation of the amount spent per owner is $12, construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class.

Answer 1

Answer: $(\ 106.29,\ \ 112.37)$

Step-by-step explanation:

Given : Sample size : $n=60$

The mean amount of money spent per owner = $\ 109.33\text{ per class}$

Standard deviation : $\sigma=\ 12$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

We know that the confidence interval for population mean is given by :-

$\mu\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$109.33\pm(1.96)\dfrac{12}{\sqrt{60}}\\\\\approx109.33\ \pm\ 3.04\\\\\approx(109.33-3.04,\ 109.33+3.04)\\\\(106.29,\ 112.37)$

Hence, the 95% confidence interval for the mean amount spent per owner for an obedience class will be $(\ 106.29,\ \ 112.37)$