Question

a personnel director in a particular state claims that the mean annual income is the same in one of the state’s counties (county a) as it is in another county (county b). in county a, a random sample of 18 residents has a mean annual income of $41,100 and a standard deviation of $8400. in county b, a random sample of 8 residents has a mean annual income of $38,400 and a standard deviation of $5700. at α = 0.10, answer parts (a) through (e). assume the population variances are not equal. assume the samples are random and independent, and the populations are normally distributed.

(a) identify the claim and state h₀ and hₐ.

which is the correct claim below?

a. \the mean annual incomes in counties a and b are not equal.\

b. \the mean annual income in county a is less than in county b.\

c. \the mean annual incomes in counties a and b are equal.\

d. \the mean annual income in county a is greater than in county b.\

Explanation:

The personnel director claims that the mean annual income is the same in County A and County B. So we need to find the option that states the means are equal. Option A says they are not equal, B says A is less than B, D says A is greater than B, while C says they are equal, which matches the claim.

Answer:

C. "The mean annual incomes in Counties A and B are equal."