Question

A company creates wooden furniture to be sold at various retailers. This company claims that only 2.53% of their furniture are defective in some manner. Monica would like to test this claim to see if the actual percentage of furniture that is defective is different than the company claims, using a = 0.05. She takes a sample of 620 pieces of furniture, and observes that 39 of these furniture pieces are defective. Assume a normal sampling distribution.

What are the null and alternative hypotheses?
H₀: p < 0.0253
Hₐ: p = 0.0253

Answer 1

The null hypothesis for Monica's test is H0: p = 0.0253, which states the proportion is equal to the company's claim. The alternative hypothesis is Ha: p ≠ 0.0253, indicating a different proportion of defects than claimed. Monica is using an alpha level of 0.05 to conduct her hypothesis test.

Step-by-step explanation:

Monica is conducting a hypothesis test to determine if the actual percentage of defective furniture differs from the company's claim of 2.53%. The null hypothesis (H0) should be the statement of no effect or no difference, so in this case, it should state that the proportion of defective furniture is equal to the claimed proportion.

Thus, the null hypothesis will be H0: p = 0.0253. On the other hand, the alternative hypothesis (Ha) represents what Monica suspects may actually be true, that the proportion of defective furniture is not 2.53%.

Therefore, the alternative hypothesis should be Ha: p ≠ 0.0253, indicating it can be either less than or greater than 2.53%. With an alpha level (α) of 0.05, Monica will assess whether to reject or fail to reject the null hypothesis based on her sample data of 620 furniture pieces with 39 defects.