Test of Association - Hat Factory: The operations manager of a company that manu

Question

Test of Association - Hat Factory: The operations manager of a company that manufactures hats wants to determine if there is an association between the shift that produced a hat and whether it is flawed or not. She randomly selects 600 recently made hats and inspects them. Each hat is classified as either perfect or flawed, and the shift that produced it is recorded. The observed sample data are in the table below. In the table above, ? is the last digit of your student ID number. For example, if your student ID number is 19406368, your sample will contain 8 flawed hats produced by the first shift and 192 perfect hats produced by the first shift. Do the data provide sufficient evidence of an association between shift and condition of hats? Hypotheses: H_0: There is no association between shift and condition of hats. H_4: There is an association between shift and condition of hats. Complete the chi-squared test of association by doing the following: (a) Determining the expected counts/cell frequencies. Since every column total is 200, each expected count simplifies to (row total)/3. It's fine with me if you round the expected counts to two places. (b) Compute the test statistic. If you want to round the components, round them to at least three places. Alternatively, if you want to use software (like Excel) for the algebra, just copy a software screenshot into your assignment with the components and test statistic visible. (c) Compute the p-value using the theoretical X" distribution on StatKey. (Don't use anything under "More Advanced Randomization Tests".) Copy a screenshot of the p-value into your assignment, and make sure you don't crop the degrees of freedom out. (d) If the significance level is alpha = 05, which of the following is the correct conclusion? 1. H_0 should be rejected. There is sufficient evidence to conclude that there is an association between shift and condition of hats. 2. H_0 should not be rejected. There is insufficient evidence to conclude that there is an association between shift and condition of hats.

Explanation / Answer

for original table:

a)

b)

test statistic X2 =0.524

c) p value =0.7693

d) 2 is correct conclusion. Ho should not be rejected.there is insufficient.........................

Observed O first second third Total perfect 192 191 189 572 flawed 8 9 11 28 Total 200 200 200 600

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