Final answer:
To determine if there is evidence to support the claim that Manufacturer 2 produces yarn with a higher mean breaking strength, we use a 90% confidence interval for the difference in means. If the interval is above zero, it indicates evidence at the 10 percent level. If it includes zero, there is insufficient evidence to support the claim.
Step-by-step explanation:
To assess whether Manufacturer 2 produces yarn with a higher mean breaking strength than Manufacturer 1, we need to conduct a hypothesis test and examine the 90% confidence interval for the difference in means. A 90% confidence interval provides an estimated range of values which is likely to include the true difference in mean breaking strength between the two manufacturers. If this interval is entirely above zero, then we can say there is evidence to support the claim that Manufacturer 2 has a higher mean breaking strength.
If we compute the 90% confidence interval and it does not include the value zero (the point of no difference), we can say that there is significant evidence at the 10 percent level since zero (the value under the null hypothesis of no difference) is not included in our interval. This would align with statement 39, which acknowledges evidence of statistical significance at the 10 percent level. However, if the interval includes zero, there would not be sufficient evidence to support the claim that Manufacturer 2 produces yarn with a higher mean breaking strength.