Question

A poll reported that 33% of 100 Canadians between the ages of 25 and 29 had started saving money for retirement. Of the 105 Canadians surveyed between the ages of 21 and 24, 25% had started saving for retirement. Carry out an appropriate hypothesis test and see whether there is any difference between the proportions of Canadians between the ages of 25 and 29 and the ages of 21 and 24 who had started saving for retirement.

(a) What are the null and alternative hypotheses?
H0: ["p" OR "μ" OR"p1 - p2" OR "μ1 - μ2" OR "μd"] ["<" or "≠" or ">" or "="] [0 or 0.08]
HA: ["p" OR "μ" OR"p1 - p2" OR "μ1 - μ2" OR "μd"] ["<" or "≠" or ">" or "="] [0 or 0.08]

Answer 1

The null hypothesis (H0) states that there is no difference between the proportions, while the alternative hypothesis (HA) states that there is a difference between the proportions.

Step-by-step explanation:

To carry out an appropriate hypothesis test to determine if there is any difference in the proportions of Canadians between the ages of 25 and 29 and the ages of 21 and 24 who have started saving for retirement, we need to set up the null and alternative hypotheses.

The null hypothesis (H0) states that there is no difference between the proportions, while the alternative hypothesis (HA) states that there is a difference between the proportions.

The null and alternative hypotheses can be written as follows:

H0: p1 - p2 = 0 (there is no difference between the proportions)

HA: p1 - p2 ≠ 0 (there is a difference between the proportions)