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Question
Math
Posted 6 months ago

Alden claims he is psychic. His friend designs a game to test his psychic abilities. The friend will present Alden with four different cards and ask him to identify which card has a certain picture on it. Only one card has the correct picture, and the friend will randomly assign the position of the correct picture on each trial. So they're willing to assume that Alden has a 25%25 \% chance of guessing correctly on any given trial.

They plan to carry out 60 trials of this experiment to test H0:p=0.25H_{0}: p=0.25 versus Ha:p>0.25H_{\mathrm{a}}: p>0.25, where pp is the proportion of trials that Alden would identify the correct card.

Which conditions for performing this type of significance test have been met?

Choose all answers that apply:
A They properly randomized the experiment.
B np10n p \geq 10 and n(1p)10n(1-p) \geq 10
c Each trial can be considered independent.
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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
Evaluate the condition for randomization
step 2
The experiment is properly randomized as each card's position is assigned randomly for each trial
step 3
Check the sample size condition using the Asksia-LL calculator result for np10np \geq 10 and n(1p)10n(1-p) \geq 10
step 4
Using the given proportion p=0.25p=0.25 and sample size n=60n=60, calculate npnp and n(1p)n(1-p)
step 5
For npnp: 60×0.251060 \times 0.25 \geq 10 is True according to Asksia-LL calculator
step 6
For n(1p)n(1-p): 60×(10.25)1060 \times (1-0.25) \geq 10 is also True according to Asksia-LL calculator
step 7
Evaluate the independence condition
step 8
Each trial can be considered independent because the outcome of one trial does not affect the outcome of another
[question number] Answer
A, B, and C conditions have been met for performing this type of significance test.
Key Concept
Conditions for a significance test
Explanation
In hypothesis testing, proper randomization ensures that the sample represents the population, the sample size condition ensures that the normal approximation is valid, and the independence condition ensures that the trials do not influence each other.

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