You are interested in purchasing a new car and have done some research. one of the many points you wish to consider is the resale value of the car after 5 years. you wish to estimate the resale value of the one that piques your interest with a 99% confidence interval. in your research, you obtain data on 17 recently resold 5-year-old sedans of the same model you wish to purchase. these 17 cars were resold at an average price of $12,500 with a standard deviation of $700. what is the 99% ci for the true mean resale value?

The 99% confidence interval would be given by (12004.26;12995.74)  

Explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s=700 represent the sample standard deviation

n=17 represent the sample size  

2) Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,16)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 99% confidence interval would be given by (12004.26;12995.74)    

answer; work samples;

disadvantages of leasing a vehicle: no vehicle equity and mileage limitations

disadvantages of purchasing a vehicle: large down payment and vehicle depreciation

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