Question

A report summarizes a survey of people in two independent random samples. One sample consisted of 700 young adults (age 19 to 35) and the other sample consisted of 400 parents of children 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.

(a) When asked about getting married, 41% of the young adults said they thought parents would provide financial support and 43% of the parents said they would provide support. Carry out a hypothesis test to determine if there is convincing evidence that the proportion of young adults who think parents would provide financial support and the proportion of parents who say they would provide support are different. (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_{young adults} − μ_parents.Round your test statistic to two decimal places and your P-value to three decimal places.)

z	=
P-value	=

State your conclusion.

We reject H₀. We do not have convincing evidence of a difference between the proportion of young adults who think that their parents would provide financial support for marriage and the proportion of parents who say they would provide financial support for marriage.

We fail to reject H₀. We do not have convincing evidence of a difference between the proportion of young adults who think that their parents would provide financial support for marriage and the proportion of parents who say they would provide financial support for marriage.    

We fail to reject H₀. We have convincing evidence of a difference between the proportion of young adults who think that their parents would provide financial support for marriage and the proportion of parents who say they would provide financial support for marriage.

We reject H₀. We have convincing evidence of a difference between the proportion of young adults who think that their parents would provide financial support for marriage and the proportion of parents who say they would provide financial support for marriage.

(b) The report stated that the proportion of young adults who thought parents would help with buying a house or apartment was 0.37. For the sample of parents, the proportion who said they would help with buying a house or 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 an apartment is significantly less than the proportion of young adults who think that their parents would help? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_{young adults} − μ_parents. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

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.   

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 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.

Answer 1

a)

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Young Adults	700	287	0.410000
parents	400	172	0.430000

Estimation for Difference

Difference	95% CI for Difference
-0.02	(-0.080674, 0.040674)

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	-0.65	0.5182

Conclusion

We fail to reject H₀. We do not have convincing evidence of a difference between the proportion of young adults who think that their parents would provide financial support for marriage and the proportion of parents who say they would provide financial support for marriage.    

b)

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Young Adults	700	259	0.370000
Parents	400	108	0.270000

Estimation for Difference

Difference	95% CI for Difference
0.1	(0.043679, 0.156321)

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	3.48	0.0005

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.