Can We Be 90% Confident That Cotton Fabric Is Unsuitable for Dyeing?

Is it possible to be 90% confident that the water pickup is less than 56% and the cotton fabric is unsuitable for dyeing?

Based on the given data, can we make this conclusion?

Analysis:

Based on the provided information, we are tasked with determining if we can be 90% confident that the water pickup is less than 56% and if the cotton fabric is unsuitable for dyeing. The data consists of a sample with a mean water pickup of 56.80% and a sample standard deviation of 4.50%.

In order to assess this situation, we can conduct a one-sample t-test to determine if the water pickup is less than 56% with 90% confidence. The formula for the test statistic involves the sample mean, population mean, sample standard deviation, sample size, and degrees of freedom.