You’re a psychologist contracted by the U.S. Navy to develop a new method to train dolphins to identify potential enemy underwater explosive devices. Using the current training method, dolphins correctly identify a mean of 82 (out of 100) targets. You claim that dolphins trained under your new method will correctly identify more targets than the prevailing standard of 82. You train 7 dolphins with your new technique and obtain the following scores of correctly identified targets (out of 100) for each dolphin: 88, 79, 92, 87, 82, 86, and 91.

Which of the following are the correct statements of the null and alternate hypotheses, H0 and HA?

a. H0: [tex]\mu = 82[/tex] and HA: [tex]\mu \neq 82[/tex]
b. H0: [tex]\mu \neq 82[/tex] and HA: [tex]\mu = 82[/tex]
c. H0: [tex]\mu > 82[/tex] and HA: [tex]\mu \leq 82[/tex]
d. H0: [tex]\mu \geq 82[/tex] and HA: [tex]\mu < 82[/tex]
e. H0: [tex]\mu < 82[/tex] and HA: [tex]\mu \geq 82[/tex]
f. H0: [tex]\mu \leq 82[/tex] and HA: [tex]\mu > 82[/tex]

Question

29-11-2024
Mathematics

High School

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You’re a psychologist contracted by the U.S. Navy to develop a new method to train dolphins to identify potential enemy underwater explosive devices. Using the current training method, dolphins correctly identify a mean of 82 (out of 100) targets. You claim that dolphins trained under your new method will correctly identify more targets than the prevailing standard of 82. You train 7 dolphins with your new technique and obtain the following scores of correctly identified targets (out of 100) for each dolphin: 88, 79, 92, 87, 82, 86, and 91.

Which of the following are the correct statements of the null and alternate hypotheses, H0 and HA?

a. H0: [tex]\mu = 82[/tex] and HA: [tex]\mu \neq 82[/tex]
b. H0: [tex]\mu \neq 82[/tex] and HA: [tex]\mu = 82[/tex]
c. H0: [tex]\mu > 82[/tex] and HA: [tex]\mu \leq 82[/tex]
d. H0: [tex]\mu \geq 82[/tex] and HA: [tex]\mu < 82[/tex]
e. H0: [tex]\mu < 82[/tex] and HA: [tex]\mu \geq 82[/tex]
f. H0: [tex]\mu \leq 82[/tex] and HA: [tex]\mu > 82[/tex]

Answer :

Final answer:

The null hypothesis (H0) for this problem is H0: μ ≤ 82, suggesting the new training method does not improve the dolphins' performance or makes it worse. On the other hand, the alternative hypothesis (HA) is HA: μ > 82, suggesting that the new training method improves the dolphins' skill in identifying underwater explosive devices.

Explanation:

In hypothesis testing, the null hypothesis (H0) represents a statement of no effect or no difference, while the alternative hypothesis (HA) is what you might believe to be true or hope to prove true.

Given your claim that dolphins trained under your new method will correctly identify more targets than the current standard of 82, the correct statements of the null and alternative hypotheses are: H0: μ ≤ 82 and HA: μ > 82. Here, μ denotes the mean score of correctly identified targets.

In simpler terms, the null hypothesis (H0) is that the new training method results in a mean score of correctly identified targets that is less than or equal to the existing standard (82), and the alternative hypothesis (HA) is that the new training method leads to a mean score that is greater than the existing standard.

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Answer :

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Explanation:

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