Respuesta :
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
b) Yes.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.
As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The conditions to met for this test are:
- The sampling method for each population is simple random sampling.
- The samples are independent.
- Each sample includes at least 10 successes and 10 failures.
[tex]\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}[/tex]
- Each population is at least 20 times as big as its sample.
This conditions are met, so all criteria for the hypothesis test is satisfied.
