A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers.To test this,the design department manager has selected a random sample of customers and shown them the first design.A second sample of customers is shown design 2.The manager then asks each customer whether they prefer the new design they were shown over the one they currently own.The following results were observed:
Based on these data and a significance level equal to 0.05,the appropriate null and alternative hypotheses are:
H₀ : ₁ ≥ ₂
H_a : ₁ < ₂

Question

A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers.To test this,the design department manager has selected a random sample of customers and shown them the first design.A second sample of customers is shown design 2.The manager then asks each customer whether they prefer the new design they were shown over the one they currently own.The following results were observed:

Based on these data and a significance level equal to 0.05,the appropriate null and alternative hypotheses are:
H₀ :

₁ ≥

₂
H_a :

₁ <

₂

Quizplus · Accepted Answer

The null hypothesis (H₀) states that there is no difference between the proportion of customers who prefer design 1 and design 2. The alternative hypothesis (H_a) states that the proportion of customers who prefer design 1 is less than the proportion who prefer design 2. This is because the manager is interested in determining whether there is a preference for one design over the other. So, the appropriate null and alternative hypotheses are as given in option A.

A Major Manufacturer of Home Electronics Is Interested in Determining