(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
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
Need help computing the z value and finding c only
![### Analyzing Red Blood Cell Volume for Medical Research
#### Context
Total blood volume (in ml) per body weight (in kg) is a critical parameter in medical research. For healthy adults, the average red blood cell volume is about \( \mu = 28 \, \text{ml/kg} \). Abnormal red blood cell volumes can indicate potential medical issues. Roger's red blood cell volumes from seven tests are given as follows:
\[ 32, \, 26, \, 42, \, 34, \, 32, \, 37, \, 31 \]
#### Given
Let \( x \) represent Roger's red blood cell volume. Assume \( x \) follows a normal distribution with a standard deviation (\( \sigma \)) of 4.75. We are tasked with determining if Roger's average red blood cell volume significantly differs from \( \mu = 28 \, \text{ml/kg} \) using a significance level of \( \alpha = 0.01 \).
#### (a) Level of Significance
The level of significance is \( \alpha = 0.01 \).
#### Hypotheses
State the null and alternate hypotheses. Determine if a left-tailed, right-tailed, or two-tailed test is appropriate.
- \( H_0 \): \( \mu = 28 \, \text{ml/kg} \); \( H_a \): \( \mu \neq 28 \, \text{ml/kg} \); two-tailed (Selected)
Options available:
- Two-tailed
- Two-tailed
- Right-tailed
- Left-tailed
#### (b) Sampling Distribution
Choose and justify the appropriate sampling distribution.
- **Selected option:** The standard normal distribution, assuming \( x \) has a normal distribution with known \( \sigma \).
Options available:
- The Student’s t, with large sample size \( n \) and unknown \( \sigma \).
- The standard normal, known \( \sigma \).
- The Student’s t, known \( \sigma \).
- The standard normal, unknown \( \sigma \).
#### Compute \( z \)-value
Calculate the \( z \) value of the sample test statistic, rounding to two decimal places. (No computation steps provided in the image).
#### (c) P-value
Find or estimate the \( P \)-value, rounding to four decimal places](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F675d7c68-68c2-40f4-bb09-6fc638745853%2F16612ae9-e7e9-4f68-9222-6cfa933c67e4%2Fix05u2j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing Red Blood Cell Volume for Medical Research
#### Context
Total blood volume (in ml) per body weight (in kg) is a critical parameter in medical research. For healthy adults, the average red blood cell volume is about \( \mu = 28 \, \text{ml/kg} \). Abnormal red blood cell volumes can indicate potential medical issues. Roger's red blood cell volumes from seven tests are given as follows:
\[ 32, \, 26, \, 42, \, 34, \, 32, \, 37, \, 31 \]
#### Given
Let \( x \) represent Roger's red blood cell volume. Assume \( x \) follows a normal distribution with a standard deviation (\( \sigma \)) of 4.75. We are tasked with determining if Roger's average red blood cell volume significantly differs from \( \mu = 28 \, \text{ml/kg} \) using a significance level of \( \alpha = 0.01 \).
#### (a) Level of Significance
The level of significance is \( \alpha = 0.01 \).
#### Hypotheses
State the null and alternate hypotheses. Determine if a left-tailed, right-tailed, or two-tailed test is appropriate.
- \( H_0 \): \( \mu = 28 \, \text{ml/kg} \); \( H_a \): \( \mu \neq 28 \, \text{ml/kg} \); two-tailed (Selected)
Options available:
- Two-tailed
- Two-tailed
- Right-tailed
- Left-tailed
#### (b) Sampling Distribution
Choose and justify the appropriate sampling distribution.
- **Selected option:** The standard normal distribution, assuming \( x \) has a normal distribution with known \( \sigma \).
Options available:
- The Student’s t, with large sample size \( n \) and unknown \( \sigma \).
- The standard normal, known \( \sigma \).
- The Student’s t, known \( \sigma \).
- The standard normal, unknown \( \sigma \).
#### Compute \( z \)-value
Calculate the \( z \) value of the sample test statistic, rounding to two decimal places. (No computation steps provided in the image).
#### (c) P-value
Find or estimate the \( P \)-value, rounding to four decimal places
Expert Solution
Step 1: Data given
32,26,42,34,32,37,31
n=7,
Step by step
Solved in 3 steps with 2 images
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