### Transcription of Statistical Problems for Educational Use #### Problem (a) - **Context**: A researcher is investigating if a specific type of hummingbird living in the Grand Canyon has a different average weight compared to the known average weight of 4.55 grams. - **Objective**: Determine the appropriate null and alternative hypotheses for the study based on a sample mean weight of 3.75 grams from 30 hummingbirds. **Hypothesis Options**: - A. \( H_0: \mu = 3.75, \quad H_a: \mu > 3.75 \) - B. \( H_0: \mu = 3.75, \quad H_a: \mu \neq 3.75 \) - C. \( H_0: \mu = 4.55, \quad H_a: \mu < 4.55 \) - D. \( H_0: \mu = 4.55, \quad H_a: \mu > 4.55 \) - E. \( H_0: \mu = 4.55, \quad H_a: \mu \neq 4.55 \) - F. \( H_0: \mu < 4.55, \quad H_a: \mu = 4.55 \) #### Problem (b) - **Context**: According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 bpm. A farmer notices a change in his dog's heart rate and reports a sample mean of 118.2 bpm, raising questions about a slowing heart rate. **Hypothesis Options**: - A. \( H_0: \mu = 115, \quad H_a: \mu < 115 \) - B. \( H_0: \mu = 115, \quad H_a: \mu \neq 115 \) - C. \( H_0: \mu = 115, \quad H_a: \mu > 115 \) - D. \( H_0: \mu = 115, \quad H_a: \mu > 115 \) - E. \( H_0: \mu = 118.2, \quad H_a: \mu \neq 118.2 \) - F. \( H_0: \bar{x} = 118.
### Transcription of Statistical Problems for Educational Use #### Problem (a) - **Context**: A researcher is investigating if a specific type of hummingbird living in the Grand Canyon has a different average weight compared to the known average weight of 4.55 grams. - **Objective**: Determine the appropriate null and alternative hypotheses for the study based on a sample mean weight of 3.75 grams from 30 hummingbirds. **Hypothesis Options**: - A. \( H_0: \mu = 3.75, \quad H_a: \mu > 3.75 \) - B. \( H_0: \mu = 3.75, \quad H_a: \mu \neq 3.75 \) - C. \( H_0: \mu = 4.55, \quad H_a: \mu < 4.55 \) - D. \( H_0: \mu = 4.55, \quad H_a: \mu > 4.55 \) - E. \( H_0: \mu = 4.55, \quad H_a: \mu \neq 4.55 \) - F. \( H_0: \mu < 4.55, \quad H_a: \mu = 4.55 \) #### Problem (b) - **Context**: According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 bpm. A farmer notices a change in his dog's heart rate and reports a sample mean of 118.2 bpm, raising questions about a slowing heart rate. **Hypothesis Options**: - A. \( H_0: \mu = 115, \quad H_a: \mu < 115 \) - B. \( H_0: \mu = 115, \quad H_a: \mu \neq 115 \) - C. \( H_0: \mu = 115, \quad H_a: \mu > 115 \) - D. \( H_0: \mu = 115, \quad H_a: \mu > 115 \) - E. \( H_0: \mu = 118.2, \quad H_a: \mu \neq 118.2 \) - F. \( H_0: \bar{x} = 118.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
For each statement, select the correct null hypothesis, H0, and alternative hypothesis, Ha, in symbolic form
Transcribed Image Text:### Transcription of Statistical Problems for Educational Use
#### Problem (a)
- **Context**: A researcher is investigating if a specific type of hummingbird living in the Grand Canyon has a different average weight compared to the known average weight of 4.55 grams.
- **Objective**: Determine the appropriate null and alternative hypotheses for the study based on a sample mean weight of 3.75 grams from 30 hummingbirds.
**Hypothesis Options**:
- A. \( H_0: \mu = 3.75, \quad H_a: \mu > 3.75 \)
- B. \( H_0: \mu = 3.75, \quad H_a: \mu \neq 3.75 \)
- C. \( H_0: \mu = 4.55, \quad H_a: \mu < 4.55 \)
- D. \( H_0: \mu = 4.55, \quad H_a: \mu > 4.55 \)
- E. \( H_0: \mu = 4.55, \quad H_a: \mu \neq 4.55 \)
- F. \( H_0: \mu < 4.55, \quad H_a: \mu = 4.55 \)
#### Problem (b)
- **Context**: According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 bpm. A farmer notices a change in his dog's heart rate and reports a sample mean of 118.2 bpm, raising questions about a slowing heart rate.
**Hypothesis Options**:
- A. \( H_0: \mu = 115, \quad H_a: \mu < 115 \)
- B. \( H_0: \mu = 115, \quad H_a: \mu \neq 115 \)
- C. \( H_0: \mu = 115, \quad H_a: \mu > 115 \)
- D. \( H_0: \mu = 115, \quad H_a: \mu > 115 \)
- E. \( H_0: \mu = 118.2, \quad H_a: \mu \neq 118.2 \)
- F. \( H_0: \bar{x} = 118.
Expert Solution
Step 1: Determine the given data
From the provided information,
A certain type of hummingbird is known to have an average weight of 4.55 grams.
The claim is that hummingbird living in the Grand Canyon differ in weight from the population as a whole.
Step by step
Solved in 5 steps with 6 images
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