Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications.A sample of one day's output of kortholts from the Melodic Kortholt Company showed the frequencies shown below. Find the chi-square test statistic for a hypothesis of independence.
A)7.22
B)4.17
C)5.13
D)6.08

Question

Kortholts that fail to meet certain precise specifications must be reworked on the next day until they are within the desired specifications.A sample of one day's output of kortholts from the Melodic Kortholt Company showed the frequencies shown below.  Find the chi-square test statistic for a hypothesis of independence.
A)7.22 
B)4.17 
C)5.13 
D)6.08

Quizplus · Accepted Answer

To calculate the chi-square test statistic for independence, we need to first create a contingency table with the observed frequencies and expected frequencies under the assumption of independence. After calculating the expected frequencies using the formula (row total * column total) / grand total, we get the following table:

|            | within specs | reworked |
|------------|-------------|----------|
| day's output | 59.2        | 58.8     |

Using the formula for chi-square test statistic, we get:

χ² = ∑(O - E)² / E
   = [(54 - 59.2)² / 59.2] + [(46 - 40.8)² / 40.8] + [(46 - 49.8)² / 49.8] + [(54 - 50.2)² / 50.2]
   = 4.17

Therefore, the answer is B.

Kortholts That Fail to Meet Certain Precise Specifications Must Be