NZ On Air commissioned a survey called "New Zealand's Identity, Culture and the Media. What's changed in 30 years?" This study included a review of a 1990 survey and a new survey in August, 2019. The respondents were asked about social issues and concerns in New Zealand.
Assume that each survey is a random sample of New Zealand adults.
The table below shows the number of people who Agree with each issue from the 1000 people surveyed in 1990 and the 1660 people surveyed in 2019.
Issue | 1990 n = 1000 | 2019 n = 1660
Social issues in NZ like suicide, poverty & homelessness are a problem | NA | 1428
NZ is the best place for raising a family | 723 | 1196
The increasing gap between the rich and the poor in NZ is a concern | NA | 1180
Religious values are an important part of NZ culture | 385 | 554
In NZ everyone has an opportunity to succeed if they work at it | 800 | 1171
It is the expectation of all NZers that they will own their own home | 783 | 800
(NA means the question was not asked in 1990 and so is not applicable)
Let
p2019 family be the proportion of all NZ adults who, in 2019, agreed that NZ is the best place for raising
p1990 family be the proportion of all NZ adults who, in 1990, agreed that NZ is the best place for raising
A two-tailed t-test for H0: p2019 - p1990 = 0 is conducted resulting in a P-value of 0.8891
Which one of the following statements is a correct interpretation of the P-value for this test?
- At the 5% level of significance, we can claim that p2019 = p1990.
- At the 1% level of significance, there is enough evidence to claim that p2019 = p1990.
- At the 5% level of significance, the difference between p̂2019 and p̂1990 is statistically significant.
- At the 5% level of significance, we do not have evidence to claim that p2019 is different from p1990.
- At the 1% level of significance, we can claim that p2019 = p1990.