A clothing manufacturer traditionally makes sweatshirts from three different fabrics, A, B and C. Over the years the percentages sold of each fabric are 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.
-Refer to Exhibit 12.4. 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

The test statistic for this problem is calculated using the chi-square goodness-of-fit test formula. The formula is:

chi-square = sum of [(observed frequency - expected frequency)^2 / expected frequency]

Using the information given in the problem, we can calculate the expected frequencies for each fabric as:
Expected frequency of fabric A = 0.5 x (6500+3400+2700) = 6300
Expected frequency of fabric B = 0.35 x (6500+3400+2700) = 4410
Expected frequency of fabric C = 0.15 x (6500+3400+2700) = 1890

Using these expected and observed frequencies, we can calculate the chi-square value as:

chi-square = [(6500-6300)^2/6300] + [(3400-4410)^2/4410] + [(2700-1890)^2/1890] = 584.81

Therefore, the answer is B.

A Clothing Manufacturer Traditionally Makes Sweatshirts from Three Different Fabrics