To test the company's claim about the color distribution of candies, we will perform a chi-square goodness-of-fit test.

Step-by-Step Solution

1. State the hypotheses:

• Null Hypothesis ($H_0$): The color distribution of the candies is as claimed by the company.
• Alternative Hypothesis ($H_1$): The color distribution of the candies is not as claimed by the company.

2. Observed Frequencies:

The observed frequencies for each color are given as:

• Red: $O_{Red} = 14$
• Orange: $O_{Orange} = 25$
• Yellow: $O_{Yellow} = 10$
• Brown: $O_{Brown} = 6$
• Blue: $O_{Blue} = 27$
• Green: $O_{Green} = 18$

3. Expected Frequencies:

The expected frequencies for each color, based on the company's claim, are:

• Red: $E_{Red} = 0.15 \times 100 = 15$
• Orange: $E_{Orange} = 0.21 \times 100 = 21$
• Yellow: $E_{Yellow} = 0.16 \times 100 = 16$
• Brown: $E_{Brown} = 0.10 \times 100 = 10$
• Blue: $E_{Blue} = 0.23 \times 100 = 23$
• Green: $E_{Green} = 0.15 \times 100 = 15$

4. Calculate the chi-square test statistic:

The chi-square test statistic is calculated using the formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$ Where $O_i$ are the observed frequencies and $E_i$ are the expected frequencies.

Calculations: