Statistics students believe that the mean score on a first statistics test is 65. The instructor thinks that the mean score is higher. She samples 10 statistics students and obtains the scores: Grades 69 68.4 64.3 64.3 73.5 74.4 73.5 88 62.7 85.5 Test grades are believed to be normally distributed. Use a significance level of 5%.
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.
![The image displays a section of a form related to hypothesis testing in statistics. Here is a transcription suitable for use on an educational website:
---
**D. State the test statistic:**
\[ t = \_\_\_\_ \]
**E. State the p-value:**
\[ \_\_\_\_ \]
**F. Decision:**
- ○ Reject the null hypothesis.
- ○ Do not reject the null hypothesis.
---
Explanation: The form includes blank fields where the test statistic (t-value) and the p-value are to be entered. In the decision section, there are radio buttons for options to either "Reject the null hypothesis" or "Do not reject the null hypothesis."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8007b36-f4a6-4b32-9d11-4a6561dde5ee%2F4072bbdb-dc20-47fa-b260-f413fddd7a61%2Fzdhpyx_processed.jpeg&w=3840&q=75)
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