A clothing manufacturer traditionally makes sweatshirts from three different fabrics: A,B and C.Over the years,the percentages sold of each fabric were 50,35,and 15,respectively.Recently,the manufacturer began producing running suits from the same three fabrics.During the first three months of production,the company received orders for 6,500 suits made from fabric A,3,400 from fabric B,and 2,700 from fabric C.What is the value of the test statistic useful for determining how well the pattern of sales (by fabric type)of the new running suit corresponds to the expected pattern?

Question

Quizplus · Accepted Answer

To determine how well the pattern of sales of the new running suit corresponds to the expected pattern, we need to use the chi-squared goodness of fit test.

The formula for the test statistic is: 
χ² = Σ[(Observed frequency - Expected frequency)²/Expected frequency]

We can fill in the values:
χ² = [(6500 - (0.5*12700))²/(0.5*12700)] + [(3400 - (0.35*12700))²/(0.35*12700)] + [(2700 - (0.15*12700))²/(0.15*12700)]
χ² = 584.81

Therefore, the value of the test statistic is 584.81. The correct answer is (B).

A Clothing Manufacturer Traditionally Makes Sweatshirts from Three Different Fabrics