A psychologist takes an SRS of \[40\] people in their twenties and \[60\] people in their fifties and surveys them about their anxieties. Suppose that \[48\%\] of people in their twenties and \[28\%\] of people in their fifties have anxiety about flying. The psychologist will then look at the difference \[(\text{20's}-\text{50's})\] between the proportions of people with anxiety about flying in each sample.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?
Choose 1 answer:
Choose 1 answer:
(Choice A)
Approximately normal, because we expect \[19.2\] successes and \[20.8\] failures from people in their twenties, and \[16.8\] and \[43.2\] from people in their fifties, and all of these counts are at least \[10\].
A
Approximately normal, because we expect \[19.2\] successes and \[20.8\] failures from people in their twenties, and \[16.8\] and \[43.2\] from people in their fifties, and all of these counts are at least \[10\].
(Choice B)
Approximately normal, because we expect \[11.2\] successes and \[28.8\] failures from people in their twenties, and \[28.8\] and \[31.2\] from people in their fifties, and all of these counts are at least \[10\].
B
Approximately normal, because we expect \[11.2\] successes and \[28.8\] failures from people in their twenties, and \[28.8\] and \[31.2\] from people in their fifties, and all of these counts are at least \[10\].
(Choice C)
Not normal, because we expect fewer than \[10\] people in their twenties with anxiety about flying.
C
Not normal, because we expect fewer than \[10\] people in their twenties with anxiety about flying.
(Choice D)
Not normal, because we expect fewer than \[10\] people in their fifties with anxiety about flying.
D
Not normal, because we expect fewer than \[10\] people in their fifties with anxiety about flying.