(a) Identify the claim and state Ho and Ha Ho: P = 11.7 H₂H # 11.7 (Type integers or decimals. Do not round.) The claim is the null hypothesis. (b) Use technology to find the P-value. Find the standardized test statistic, t. (Round to two decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
Question

16

### Statistical Hypothesis Testing Example

An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 32 dive durations has a mean of 12.2 minutes and a standard deviation of 2.1 minutes. At α = 0.10, is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

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#### (a) Identify the claim and state H₀ and Hₐ

- Null Hypothesis (H₀): \[ \mu = 11.7 \]
- Alternative Hypothesis (Hₐ): \[ \mu \ne 11.7 \]
  (Type integers or decimals. Do not round.)

The claim is the \[ \text{null} \] hypothesis.

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#### (b) Use technology to find the P-value. Find the standardized test statistic, t.

- t = \[ \_\_\_\_ \]
  (Round to two decimal places as needed.)

----

This structured approach guides you to formulate the null and alternative hypotheses, identify the claim, and calculate the standardized test statistic and P-value. This is an essential part of hypothesis testing in statistics.
Transcribed Image Text:### Statistical Hypothesis Testing Example An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 32 dive durations has a mean of 12.2 minutes and a standard deviation of 2.1 minutes. At α = 0.10, 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 H₀ and Hₐ - Null Hypothesis (H₀): \[ \mu = 11.7 \] - Alternative Hypothesis (Hₐ): \[ \mu \ne 11.7 \] (Type integers or decimals. Do not round.) The claim is the \[ \text{null} \] hypothesis. ---- #### (b) Use technology to find the P-value. Find the standardized test statistic, t. - t = \[ \_\_\_\_ \] (Round to two decimal places as needed.) ---- This structured approach guides you to formulate the null and alternative hypotheses, identify the claim, and calculate the standardized test statistic and P-value. This is an essential part of hypothesis testing in statistics.
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