A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given value and use the z-score to determine whether the value is significant Consider a score to be significant if its z-score is less than - 2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. -1.6, not significant O B. -1.6; significant O A. O C. - 17.6, significant O D. 1.6, not significant
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Understanding Z-Scores for Significance Testing**
A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given value and use the z-score to determine whether the value is significant. Consider a score to be significant if its z-score is less than −2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary.
**Options:**
- A. -1.6, not significant
- B. 1.6, significant
- C. -1.7, significant
- D. 1.6, not significant
Click to select your answer.
(Note: There are no graphs or diagrams included in this image.)
To solve this problem, follow these steps:
1. Compute the z-score using the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the score we are trying to evaluate (48.4)
- \( \mu \) is the mean (66)
- \( \sigma \) is the standard deviation (11)
2. Substitute the values into the formula:
\[
z = \frac{48.4 - 66}{11} = \frac{-17.6}{11} \approx -1.6
\]
3. Determine significance:
- Since the z-score is -1.6, it does not fall in the range of less than -2.00 or greater than 2.00.
Conclusion: The closest answer is **A. -1.6, not significant**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfee8bd7-64cb-4926-ae94-da8de32adf44%2F58760651-7e13-49bc-8e2a-25de12144395%2F6xvcyyxq_processed.jpeg&w=3840&q=75)
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