Question

In a recent sample of 85 used cars sales costs, the sample mean was $6,925 with a standard deviation of $3,159. Assume the underlying distribution is approximately normal.
a. what is the random x variable
b.Construct a 95% confidence interval for the population mean cost of a used car.
(i) State the confidence interval. (Round your answers to one decimal place.)
sketch the graph a/2= CL=
Calucate error bound

Answer 1

Let  the random variable $X$ be the cost of a used car.

The provided sample mean is $\bar{X}=6925$ and the sample standard deviation is $s=3159.$ The size of the sample is $n=85$ and the required confidence level is 95%.

The number of degrees of freedom are $df=85-1=84,$ and the significance level is $\alpha=0.05.$

Based on the provided information, the critical t-value for $\alpha=0.05$ and $df=84$

degrees of freedom is $t_c=1.9886.$ The 95% confidence for the population $\mu$  is computed using the following expression

$$CI=(\bar{X}-\dfrac{t_c\times s}{\sqrt{n}}, \bar{X}+\dfrac{t_c\times s}{\sqrt{n}})=$$

$$=(6925-\dfrac{1.9886\times 3159}{\sqrt{85}}, 6925+\dfrac{1.9886\times 3159}{\sqrt{85}})=$$

$$=(6243.62, 7606.38)$$

$EBM=\dfrac{t_c\times s}{\sqrt{n}}=\dfrac{1.9886\times 3159}{\sqrt{85}}=681.38$