Question

A manufacturer of assembly line machines is considering two varieties of titanium alloy for one of its high-stress components. They subject 32 components of each variety to continuous use and measure how long the component takes to fail each time. The mean time until failure of the sample of Alloy A was 782.875 hours with a standard deviation of 51.62 hours, and the mean time until failure of the sample of Alloy B was 831.7188 hours with a standard deviation of 51.62 hours, and the mean time until failure of the sample of Alloy B was 831.7188 hours with a standard deviation of 77.45 hours. The p-value of Levene’s test was less than .05.

Determine the correct value of the test statistic to two decimal places.

Answer 1

The question is not answerable as-is because it asks for a test statistic value without providing sufficient information to calculate it. However, the significance of Levene's test indicates a difference in variances between the two samples of titanium alloys.

Step-by-step explanation:

The student has provided data from a study comparing the lifespan of components made from two different titanium alloys. Since the p-value from Levene's test is less than 0.05, we reject the null hypothesis, indicating that there is a statistically significant difference in variability between the two samples. However, the student's question seems to be asking for a test statistic value, which generally comes from a specific statistical test such as a t-test or an F-test. Since they've mentioned Levene's test, that is a measure of equality of variance, we cannot calculate the exact test statistic without additional information, such as the value of the F-ratio or the means of the absolute deviations from the median. As the data for these calculations is not provided, we cannot calculate the test statistic here.