A report summarizes a survey of people in two independent random samples. One sa

Question

A report summarizes a survey of people in two independent random samples. One sample consisted of 500 young adults (age 19 to 35) and the other sample consisted of 200 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 = 0.05. Use a statistical computer package to calculate the P-value. Use young adults parents. Round your test statistic to two decimal places and your P-value to three decimal places.)

=

(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 = 0.05. Use a statistical computer package to calculate the P-value. Use young adults parents. Round your test statistic to two decimal places and your P-value to four decimal places.)

z = P-value

=

Explanation / Answer

a) The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

z = -0.49

P - value = 0.6277

b) The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

Hence,

z = 2.52

P - value = 0.0059

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 205 500 86 200 -0.02 0.041234348 -0.48503253 0.6277

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