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 *p*_{1} be the proportion of all
parents of young adults who say they would help with buying a house
or renting an apartment, and *p*_{2} be the
proportion of young adults who think that their parents would
help.)

State the appropriate null and alternative hypotheses.

*H*_{0}: *p*_{1}
− *p*_{2} < 0

*H*_{a}:
*p*_{1} − *p*_{2}
> 0

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2}
< 0

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2} ≠
0

*H*_{0}: *p*_{1}
− *p*_{2} > 0

*H*_{a}:
*p*_{1} − *p*_{2}
< 0

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2}
> 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 *H*_{0}. 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 *H*_{0}. 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 *H*_{0}. 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 *H*_{0}. 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,

*H*_{0}: *p*_{1}
− *p*_{2} = 0

*H*_{a}:
*p*_{1} − *p*_{2}
< 0

z = -3.11

P - value = 0.0009

Conclusion: We reject *H*_{0}. 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.

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