Interpret the key results for Bootstrapping for 1-sample function

Complete the following steps to interpret a 1-sample function bootstrapping analysis. Key output includes the histogram, the estimate of the parameter, and the confidence interval.

Step 1: Examine the shape of your bootstrap distribution

Use the histogram to examine the shape of your bootstrap distribution. The bootstrap distribution is the distribution of the chosen statistic from each resample. The bootstrap distribution should appear to be normal. If the bootstrap distribution is non-normal, you cannot trust the bootstrap results.
50 resamples
1000 resamples

The distribution is usually easier to determine with more resamples. For example, in these data, the distribution is ambiguous for 50 resamples. With 1000 resamples, the shape looks approximately normal.

In this histogram, the bootstrap distribution does not appear to be normal. The original sample has only 16 data points. To get a reliable confidence interval, you should collect a larger sample and perform the analysis again.

Step 2: Determine a confidence interval for the population parameter

First, consider the statistic from the bootstrap sample, and then examine the confidence interval.

The statistic of the bootstrap sample is an estimate of the population parameter. Because the statistic is based on sample data and not the entire population, it is unlikely that the sample statistic equals the population parameter. To better estimate the population parameter, use the confidence interval.

Confidence intervals are based on the sampling distribution of a statistic. If a statistic has no bias as an estimator of a parameter, its sampling distribution is centered at the true value of the parameter. A bootstrapping distribution approximates the sampling distribution of the statistic. Therefore, the middle 95% of values from the bootstrapping distribution provide a 95% confidence interval for the parameter. The confidence interval helps you assess the practical significance of your estimate for the population parameter. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation.

Note

Minitab does not calculate the confidence interval when the number of resamples is too small to obtain an accurate confidence interval.

Bootstrapping for 1-Sample Mean: Time

Bootstrap Histogram for Time

Observed Sample Variable N Mean StDev Variance Sum Minimum Median Maximum Time 16 11.331 3.115 9.702 181.300 7.700 10.050 16.000
Bootstrap Samples for Mean Number of Resamples Mean StDev 95% CI for μ 1000 11.3095 0.7625 (9.8562, 12.8562)
Key Results: Average, 95% Confidence Interval

In these results, the estimate for the population mean is approximately 11.3. You can be 95% confident that the population mean is between approximately 9.9 and 12.9.

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