Question

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign​ sedan, you decide to estimate the resale value of this car with a 95​% confidence interval. You manage to obtain data on 17 recently resold​ 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $ 12 comma 100 with a standard deviation of $ 800. What is the 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model?

Answer 1

Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

$(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )$

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

$t_{(16 , 0.05)} = 2.1199$

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

$(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )$

$(12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )$

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)