Questions: Nicholas is a dolphin who lives in the Clearwater Marine Aquarium in Florida. Nicholas has made predictions about 27 different sporting events including World Series, Super Bowls, and World Cup finals since 2017, and he has picked the correct winner 16 times and picked the loser to win 11 times. Sports bettors are interested in determining whether Nicholas is truly a "psychic" animal who knows something about the results of sporting events before they happen. Question 4 2 pts The null hypothesis is that [Select] and it can be written mathematically as [Select] [Select] [Select] [Select] [Select] The alternative hypothesis is that [Select] and it can be written mathematically as [Select] [Select] [Select] [Select]

Nicholas is a dolphin who lives in the Clearwater Marine Aquarium in Florida. Nicholas has made predictions about 27 different sporting events including World Series, Super Bowls, and World Cup finals since 2017, and he has picked the correct winner 16 times and picked the loser to win 11 times. Sports bettors are interested in determining whether Nicholas is truly a "psychic" animal who knows something about the results of sporting events before they happen.

Question 4
2 pts

The null hypothesis is that [Select] and it can be written mathematically as [Select] [Select] [Select] [Select] [Select] The alternative hypothesis is that [Select] and it can be written mathematically as [Select] [Select] [Select] [Select]

Transcript text: Nicholas is a dolphin who lives in the Clearwater Marine Aquarium in Florida. Nicholas has made predictions about 27 different sporting events including World Series, Super Bowls, and World Cup finals since 2017, and he has picked the correct winner 16 times and picked the loser to win 11 times. Sports bettors are interested in determining whether Nicholas is truly a "psychic" animal who knows something about the results of sporting events before they happen. Question 4 2 pts The null hypothesis is that $\square$ [Select] and it can be written mathematically as [Select] $\square$ [Select] $\square$ [Select] [Select] $\square$ The alternative hypothesis is that [Select] $\square$ and it can be written mathematically as [Select] $\square$ [Select] [Select] [Select]

Solution

Solution Steps

To determine whether Nicholas is truly a "psychic" animal, we can perform a hypothesis test. The null hypothesis (H0) is that Nicholas is guessing randomly, meaning the probability of picking the correct winner is 0.5. The alternative hypothesis (H1) is that Nicholas is not guessing randomly, meaning the probability of picking the correct winner is not 0.5.

Step 1: Define the Null Hypothesis

The null hypothesis ($H_0$) is a statement that there is no effect or no difference, and it is the hypothesis that researchers typically try to disprove. In this context, the null hypothesis is that Nicholas is not a "psychic" and his predictions are no better than random guessing.

Mathematically, if Nicholas is guessing randomly, the probability of picking the correct winner is 0.5. Therefore, the null hypothesis can be written as: \[ H_0: p = 0.5 \]

Step 2: Define the Alternative Hypothesis

The alternative hypothesis ($H_1$) is a statement that indicates the presence of an effect or a difference. In this context, the alternative hypothesis is that Nicholas is a "psychic" and his predictions are better than random guessing.

Mathematically, this can be written as: \[ H_1: p \neq 0.5 \]

Final Answer

The null hypothesis is that Nicholas is not a "psychic" and his predictions are no better than random guessing. It can be written mathematically as: \[ \boxed{H_0: p = 0.5} \]

The alternative hypothesis is that Nicholas is a "psychic" and his predictions are better than random guessing. It can be written mathematically as: \[ \boxed{H_1: p \neq 0.5} \]

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