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 90% 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 $12,580 with a standard deviation of $700. What is the 90% confidence
Interval for the true mean resale value of a 5- year-old car of this model?
A) $12,580 \pm 1.746 ( 700 / \sqrt { 17 } )$
B) $12,580 \pm 1.746 ( 700 / \sqrt { 16 } )$
C) $12,580 \pm 1.645 ( 700 / \sqrt { 17 } )$
D) $12,580 \pm 1.740 ( 700 / \sqrt { 17 } )$

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 90% 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 $12,580 with a standard deviation of $700. What is the 90% confidence
Interval for the true mean resale value of a 5- year-old car of this model? 
A) $12,580 \pm 1.746 ( 700 / \sqrt { 17 } )$
B) $12,580 \pm 1.746 ( 700 / \sqrt { 16 } )$
C) $12,580 \pm 1.645 ( 700 / \sqrt { 17 } )$
D) $12,580 \pm 1.740 ( 700 / \sqrt { 17 } )$

Quizplus · Accepted Answer

The correct formula for a confidence interval is $\bar{x} \pm t_{\alpha/2} \left( \frac{s}{\sqrt{n}} \right)$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score for the desired confidence level with $n-1$ degrees of freedom. For a 90% confidence interval with 17 samples (16 degrees of freedom), the closest t-score is approximately 1.746. Therefore, choice A correctly applies this formula with the given data.

You Are Interested in Purchasing a New Car 12,580±1.746(700/17)12,580 \pm 1.746 ( 700 / \sqrt { 17 } )12,580±1.746(700/17​)

You Are Interested in Purchasing a New Car $12,580 \pm 1.746 ( 700 / \sqrt { 17 } )$