Question

sample daat reflects shipments received from 3 different vendors Vendor Defective Acceptable 1 16 133 2 25 74 3 24 187 what is correct hypothesis to determine if quality is associated with vendor calculate the value of the test statistic specifiy decision rule at the 1% significance level What is your conclusion

Answer 1

Question: What is the correct hypothesis to determine if quality is associated with vendor?

By looking at other resources, I have found the choices given for this question. They are the following:

a. Null: Quality and source of shipment (vendor) are independent; Alternative: Quality and source of shipment (vendor) are dependent.
b. Null: Quality and source of shipment (vendor) are dependent; Alternative: Quality and source of shipment (vendor) are independent.

The test that would be applicable for this type of data would be the Chi-Square Test for Independence. As the name implies, the null hypothesis should be that the two factors are independent since that will be what we will be testing for.

ANSWER: a. Null: Quality and source of shipment (vendor) are independent; Alternative: Quality and source of shipment (vendor) are dependent.

Question: Calculate the value of the test statistic.

Please refer to the attached document for the complete computation for this part. Generally, we need to find the expected value for each cell in the table and perform some calculation explained in the document.

ANSWER: The test statistic is 12.80.

Question: Specify decision rule at the 1% significance level.

We can get the critical value for Chi-square tests by first looking for the degree of freedom. We can get the df by evaluating the following expression: (rows-1)*(columns-1). In our case, the number of columns is 2 and the number of rows is 3. The df is therefore (2-1)(3-1)=(1)(2)=2.

We then look at a table to determine what the value at the 1% significance level and df of 2 is.

ANSWER: We reject the null hypothesis if the test statistic is greater than the critical value which is 9.2103.

Question: What is your conclusion?

Since the test statistic (12.80) is greater than the critical value (9.2103), we can therefore tell that it is in the area for rejection.

Thus, we reject the null hypothesis.

ANSWER: There is enough evidence to conclude that the quality and source of shipment (vendor) are NOT independent.

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