Practise interpreting ordered differences in population proportions and using confidence intervals to justify claims about direction and statistical evidence.
In a simple random sample (SRS) of 625 families who do not live near any chemical plant, 10 had children with leukemia. In an SRS of 412 families living near chemical plants, 15 had children with leukemia. A 90\% confidence interval of the difference in proportions is reported to be −0.0204±0.0173. What is a proper conclusion?
The interval is invalid because probabilities cannot be negative.
Families living near chemical plants are approximately 2.04\% more likely to have children with leukemia than families who do not live near any chemical plant.
Ninety percent of families living near chemical plants are approximately 2.04\% more likely to have children with leukemia than families who do not live near any chemical plant.
We are 90% confident that the difference in proportions between families who do not live near any chemical plant having children with leukemia and families who live near chemical plants having children with leukemia is between -0.0377 and -0.0031.
D
Researchers from a national research organization investigated which platform (television, social media, newspaper, In ternet, etc.) United States adults prefer to use to obtain their news. In 2016, of the 200 randomly selected United States adults that were surveyed, 114 selected television as their preferred platform. In 2018, of the 200 randomly selected United States adults that were surveyed, 98 selected television as their preferred platform. The conditions for inference are met. A 95 percent confidence interval for the difference in the population proportions of United States adults that use television as their preferred platform for obtaining news between 2016 and 2018 (2016 minus 2018) was found to be (-0.02, 0.18). Based on the interval, is it reasonable for the researchers to claim that there is convincing statistical evidence that the population proportion of United States adults that use television as their preferred method to obtain news differed between 2016 and 2018?
No, because the researchers should have used a greater confidence level to obtain convincing evidence.
No, because zero is included in the interval there is not convincing statistical evidence that the population proportion differed between 2016 and 2018.
Yes, because zero is included in the interval there is convincing statistical evidence that the population proportion differed between 2016 and 2018.
Yes, because most of the interval is positive there is convincing statistical evidence that the population proportion increased from 2016 to 2018.
Yes, because 0.57 is greater than 0.49 there is convincing statistical evidence that the population proportion decreased from 2016 to 2018.
B