Question

A report summarizes a survey of people in two independent random samples. One sample consisted of 800 young adults (age 19 to 35), and the other sample consisted of 300 parents of young adults age 19 to 35. The young adults were presented with a variety of situations (such as getting married or buying a house) and were asked if they thought that their parents were likely to provide financial support in that situation. The parents of young adults were presented with the same situations and asked if they would be likely to provide financial support to their child in that situation.

The report stated that the proportion of young adults who thought their parents would help with buying a house or renting an apartment for the sample of young adults was 0.37. For the sample of parents, the proportion who said they would help with buying a house or renting an apartment was 0.27. Based on these data, can you conclude that the proportion of parents who say they would help with buying a house or renting an apartment is significantly less than the proportion of young adults who think that their parents would help? Test the appropriate hypotheses using a significance level of 0.05. (Let p₁ be the proportion of all parents of young adults who say they would help with buying a house or renting an apartment, and p₂ be the proportion of young adults who think that their parents would help.)

State the appropriate null and alternative hypotheses.

H₀: p₁ − p₂ < 0

H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ < 0

    

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ ≠ 0

H₀: p₁ − p₂ > 0

H_a: p₁ − p₂ < 0

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ > 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State your conclusion.

We fail to reject H₀. We do not have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help.

We reject H₀. We have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help.    

We reject H₀. We do not have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help.

We fail to reject H₀. We have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help.

Answer 1

The statistical software output for this problem is:

Hence,

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ < 0

z = -3.11

P - value = 0.0009

Conclusion: We reject H₀. We have convincing evidence that the proportion of parents who say they would help with buying a house or apartment is less than the proportion of young adults who think that their parents would help.