A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.

• A. $H_0:$ $\sigma=0.300$ g$H_{a}:$ $\sigma>0.300$ g
• B. $H_0:$ $\sigma=0.300$ g$H_{a}:$ $\sigma\ne0.300$ g
• C. $H_0:$ $\sigma=0.300$ g$H_{a}:$ $\sigma$ < $0.300$ g
• D. $H_0:$ $\sigma>0.300$ g$H_{a}:$ $\sigma$ < $0.300$ g

Answer: (C)

Verified step by step guidance

1. Identify the parameter of interest, which in this case is the standard deviation of the candy weights, denoted as σ.
2. Understand the claim made by the manufacturer: they claim the standard deviation is less than 0.300 g.
3. Formulate the null hypothesis (H0). The null hypothesis is typically a statement of no effect or no difference. Here, it would be that the standard deviation is equal to 0.300 g, i.e., H0: σ = 0.300 g.
4. Formulate the alternative hypothesis (Ha). The alternative hypothesis is what you want to test for. Since the manufacturer claims the standard deviation is less than 0.300 g, the alternative hypothesis would be Ha: σ < 0.300 g.
5. Ensure the hypotheses are correctly structured for a one-tailed test, as the claim is directional (less than). The null hypothesis assumes no change or effect, while the alternative hypothesis reflects the manufacturer's claim.