An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes, A random sample of 36 dive durations has a mean of 12.3 minutes and a standard deviation of 2.1 minutes. At a =0.01 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H, and H Ho Ha (Type integers or decimals. Do not round.) The claim is the V hypothesis.

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### Problem Statement

An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 36 dive durations has a mean of 12.3 minutes and a standard deviation of 2.1 minutes. At \(\alpha = 0.01\), is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

### (a) Identify the claim and state \( H_0 \) and \( H_a \)

- \( H_0 \) (null hypothesis): [Not specified]
- \( H_a \) (alternative hypothesis): [Not specified]

*(Type integers or decimals. Do not round.)*

The claim is the [Not specified] hypothesis.

### Explanation

This question prompts the reader to identify and state the null and alternative hypotheses based on the oceanographer's claim. The claim to be tested is whether the mean dive duration is 11.7 minutes.

The null hypothesis (\( H_0 \)) typically represents the assumption of no effect or no difference, whereas the alternative hypothesis (\( H_a \)) represents what the researcher seeks to prove. In hypothesis testing, if the data provides sufficient evidence, the null hypothesis can be rejected in favor of the alternative.

### Important Points to Consider

- **Mean Value:** The sample mean is 12.3 minutes. 
- **Standard Deviation:** The population standard deviation is 2.1 minutes.
- **Sample Size:** 36 dive durations were sampled.
- **Significance Level (\(\alpha\))**: 0.01, meaning there is a 1% risk of concluding that a difference exists when there is no actual difference.

Given these inputs, the reader is guided to set up hypotheses:
- Claim (potential \( H_0 \)): The mean is 11.7 minutes.
- Alternative (\( H_a \)): The mean is not 11.7 minutes (this could be two-tailed, greater than, or less than).

Proceed with hypothesis testing calculations to determine if the claim is supported or refuted by the sample data.
Transcribed Image Text:### Problem Statement An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 36 dive durations has a mean of 12.3 minutes and a standard deviation of 2.1 minutes. At \(\alpha = 0.01\), is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. ### (a) Identify the claim and state \( H_0 \) and \( H_a \) - \( H_0 \) (null hypothesis): [Not specified] - \( H_a \) (alternative hypothesis): [Not specified] *(Type integers or decimals. Do not round.)* The claim is the [Not specified] hypothesis. ### Explanation This question prompts the reader to identify and state the null and alternative hypotheses based on the oceanographer's claim. The claim to be tested is whether the mean dive duration is 11.7 minutes. The null hypothesis (\( H_0 \)) typically represents the assumption of no effect or no difference, whereas the alternative hypothesis (\( H_a \)) represents what the researcher seeks to prove. In hypothesis testing, if the data provides sufficient evidence, the null hypothesis can be rejected in favor of the alternative. ### Important Points to Consider - **Mean Value:** The sample mean is 12.3 minutes. - **Standard Deviation:** The population standard deviation is 2.1 minutes. - **Sample Size:** 36 dive durations were sampled. - **Significance Level (\(\alpha\))**: 0.01, meaning there is a 1% risk of concluding that a difference exists when there is no actual difference. Given these inputs, the reader is guided to set up hypotheses: - Claim (potential \( H_0 \)): The mean is 11.7 minutes. - Alternative (\( H_a \)): The mean is not 11.7 minutes (this could be two-tailed, greater than, or less than). Proceed with hypothesis testing calculations to determine if the claim is supported or refuted by the sample data.
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