Question

A cruise ship charges passengers $3 for a can of soda. Because of passenger complaints, the ship manager has decided to try out a plan with a lower price. He thinks that with a lower price, more cans will be sold, which would mean that the ship would still make a reasonable total profit. With the old pricing, the mean number of cans sold per passenger for a 10-day trip was 10.3 cans.

Suppose μ represents the mean number of cans per passenger for the new pricing. What hypotheses should the ship manager test if he wants to determine if the mean number of cans sold is higher for the new pricing plan?

A H₀: μ = 10.3 versus H_a: μ ≠ 10.3
B H₀: μ = 10.3 versus H_a: μ < 10.3    
C H₀: μ = 10 versus H_a: μ < 10
D H₀: μ = 10 versus H_a: μ > 10.3
E H₀: μ = 10.3 versus H_a: μ > 10.3

Answer 1

Null hypothesis (H₀)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

Alternative Hypothesis (H₁)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

With the old pricing, the mean number of cans sold per passenger for a 10-day trip was 10.3 cans

: the mean number of cans sold per passenger for a 10-day trip

The manager wants to determine if the mean number of cans sold is higher for the new pricing plan i.e > 10.3

So, therefore,

Ans :

E. H₀: = 10.3 versus H_a: > 10.3