Final answer:
To compare the bootstrap confidence interval to the t-interval in a collision involving mini- and micro-vehicles using a bootstrap sample with 200 resamples, you need to calculate both intervals. The bootstrap interval is calculated by taking a bootstrap sample from the original data set, calculating the mean for each resample, and finding the lower and upper bounds using percentiles. The t-interval is calculated using the sample mean, sample standard deviation, t-value, and margin of error. Comparing the two intervals will provide insights into their differences and how they estimate the population mean.
Step-by-step explanation:
The question asks you to compare the bootstrap confidence interval to the t-interval in a collision involving mini- and micro-vehicles using a bootstrap sample with 200 resamples.
To calculate the bootstrap confidence interval:
- Take a bootstrap sample with replacement from the original data set.
- Calculate the mean of each bootstrap sample.
- Repeat steps 1 and 2 for a total of 200 resamples.
- Order the means of the resamples from smallest to largest.
- Calculate the lower and upper bounds of the bootstrap interval by finding the 2.5th and 97.5th percentiles of the resample means.
To calculate the t-interval:
- Calculate the sample mean and sample standard deviation of the original data set.
- Find the appropriate t-value for a two-tailed 95 percent confidence interval with the degrees of freedom for the study.
- Calculate the margin of error by multiplying the t-value by the standard deviation divided by the square root of the sample size.
- Calculate the lower and upper bounds of the t-interval by subtracting and adding the margin of error to the sample mean.
Comparing the two intervals will give you an understanding of how the bootstrap confidence interval and the t-interval differ in estimating the true value of the population mean.