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 $12,630 with a standard deviation of $800. Suppose that the interval is calculated to be ($12,291.23, $12,968.77). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval?

First way: Reduce the level of confidence. This drops the error value, since we are saying we are less confidence in the interval, we can have a smaller interval. Say we drop it to 80%, that means that we are only 80% confident that we are correct, so we're admitting to being wrong 20% of the time.

Second way: Increasing the sample size will reduce the error value, which will decrease the interval.

Third way: Reduce the level of confidence and increase the sample size. This is a combination of both previous methods.

AFOKE88 AFOKE88 · Answer 2 · 2022-04-12T14:58:44+02:00

The ways in which we could ensure the width of the interval is decreased are to; lower confidence level and increase sample size.

What is the confidence interval?

Formula for confidence interval is;

CI = x' ± z(σ/√n)

where;

x' is sample mean

z is critical value at confidence level

σ is standard deviation

n is sample size

1) Normally, the lesser the level of confidence, the lesser the critical value and ultimately the lesser the margin of error which means a decrease in the width of the interval.

2) Another way to decrease the width of interval is to Increase the sample size because it will lead to a lesser margin of error.

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