The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is _____.

To test the producer's claim about the standard deviation, you would typically use the chi-square (χ²) test for variance. Since we're dealing with a sample and trying to make inferences about the population variance from that sample, we need to use the sample standard deviation to estimate the population standard deviation.

The formula for the test statistic in a chi-square test for variance is:

χ² = (n - 1) * s² / σ²

where: - χ² is the chi-square test statistic, - n is the sample size, - s² is the sample variance (which is the square of the sample standard deviation, s), - σ² is the claimed population variance (which is the square of the claimed population standard deviation, σ).

Given the following: - n = 20 (the number of bottles sampled), - s = 0.11 ounces (the sample standard deviation), - σ = 0.1 ounces (the claimed population standard deviation).

First, we need to calculate the sample variance (s²): s² = (0.11 ounces)² = 0.0121 ounces²

Then, calculate the claimed population variance (σ²): σ² = (0.1 ounces)² = 0.01 ounces²

Now, plug the values into the formula to find the test statistic: χ² = (20 - 1) * (0.0121 ounces²) / (0.01 ounces²) χ² = 19 * 1.21 χ² = 22.99

So, the test statistic (χ²) to test the producer's claim is approximately 22.99.