You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.16. Thus you are performing a left-tailed test. Your sample data produce the test statistic z = -2.963. Find the p-value accurate to 4 decimal places. p-value
You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.16. Thus you are performing a left-tailed test. Your sample data produce the test statistic z = -2.963. Find the p-value accurate to 4 decimal places. 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
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![### Statistical Test for True Negative Probability
**Problem Statement:**
You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.16. Thus, you are performing a left-tailed test. Your sample data produce the test statistic \( z = -2.963 \). Find the p-value accurate to 4 decimal places.
**Calculation:**
To find the p-value:
1. Use the z-score of -2.963.
2. Look up the z-score in a standard normal distribution table or use statistical software/calculator to find the corresponding p-value.
**Answer:**
\( \text{p-value} = \) [Calculated p-value]
### Notes:
- **Left-Tailed Test:** This test checks if the actual parameter is significantly less than the hypothesized parameter.
- **Z-Score:** The z-score represents how many standard deviations an element is from the mean. In this problem, \( z = -2.963 \) indicates that the sample mean is 2.963 standard deviations below the hypothesized mean.
For students: Understanding how to interpret and calculate p-values in hypothesis testing is crucial in making statistically informed decisions. The p-value helps determine the significance of your results in the context of your study.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51fab9e4-c55b-4f18-999a-c6ac10434c60%2Fa00887cf-50d5-4130-9d41-443aff076d08%2Fi1au1vo_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Test for True Negative Probability
**Problem Statement:**
You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.16. Thus, you are performing a left-tailed test. Your sample data produce the test statistic \( z = -2.963 \). Find the p-value accurate to 4 decimal places.
**Calculation:**
To find the p-value:
1. Use the z-score of -2.963.
2. Look up the z-score in a standard normal distribution table or use statistical software/calculator to find the corresponding p-value.
**Answer:**
\( \text{p-value} = \) [Calculated p-value]
### Notes:
- **Left-Tailed Test:** This test checks if the actual parameter is significantly less than the hypothesized parameter.
- **Z-Score:** The z-score represents how many standard deviations an element is from the mean. In this problem, \( z = -2.963 \) indicates that the sample mean is 2.963 standard deviations below the hypothesized mean.
For students: Understanding how to interpret and calculate p-values in hypothesis testing is crucial in making statistically informed decisions. The p-value helps determine the significance of your results in the context of your study.
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