College

Terrell's company sells candy in packs that are supposed to contain 50% red candies, 25% orange, and 25% yellow. He randomly selected a pack containing 16 candies and counted how many of each color were in the pack. Here are his results:

| Color | Observed counts |
|--------|-----------------|
| Red | 9 |
| Orange | 5 |
| Yellow | 2 |

He wants to use these results to carry out a [tex]$\chi^2$[/tex] goodness-of-fit test to determine if the color distribution disagrees with the target percentages. Which count(s) make this sample fail the large counts condition for this test? Choose 2 answers:

A. The observed count of yellow candies.
B. The observed count of orange candies.

Answer :

Final answer:

In the [tex]X^2[/tex] goodness-of-fit test for the candy pack, the observed count of yellow candies (2) fails the large counts condition, as it is less than the expected count of 4.

Explanation:

The student has carried out a [tex]X^2[/tex] goodness-of-fit test using a candy pack to determine if the color distribution of the candies matches the target percentages. The large counts condition for this test requires that all expected counts are at least 5. Given that the pack is supposed to contain 50% red, 25% orange, and 25% yellow candies, the expected counts for a pack of 16 candies would be 8 for red, 4 for orange, and 4 for yellow.

The counts that make this sample fail the large counts condition are:

A. The observed count of yellow candies (2), which is less than the expected count (4).

B. The observed count of orange candies (5) does not violate the condition, as it's equal to the expected count.

Therefore, only the observed count of yellow candies makes the sample fail the large counts condition.

the expected orange

and

the expected yellow

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