A factory manager needs to understand how many products are defective versus how many are produced. The number of expected defects is listed in Table.

A random sample was taken to determine the actual number of defects. Table 11.6 shows the results of the survey.

State the null and alternative hypotheses needed to conduct a goodness-of-fit test, and state the degrees of freedom.

A factory manager needs to understand how many products are defective versus how many are produced. The number of expected defects is listed in the below given table:

A random sample was taken to determine the actual number of defects. The given table shows the results of the survey;

The null hypothesis can be stated as:

\(H_{0}:\)The number of defaults fits expectations

And the alternative hypothesis can be stated as:

\(H_{a}:\) The number of defaults does not fit expectations

In the given case, it is best to apply goodness-of-fit test because all entries are greater than or equal to five.

Therefore, the degree of freedom can be calculated as shown below;

degree of freedom\(=df=number of cells -1\)

\(=5-1=4\)

The null hypothesis can be stated as:

\(H_{0}:\) The number of defaults fits expectations

And the alternative hypothesis can be stated as:

\(H_{a}:\) The number of defaults does not fit expectations

And the degree of freedom \(= 4\).