Answered: Which of the following decisions do we… | bartleby

MATLAB: An Introduction with Applications

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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**Question:**
Which of the following decisions do we arrive at if the p-value < α level of significance?

- ○ Reject the null hypothesis
- ○ Accept the alternative hypothesis
- ○ Fail to reject the alternative hypothesis
- ○ Fail to reject the alternative hypothesis

**Explanation:**
This is a question about hypothesis testing. When conducting a hypothesis test, a small p-value (less than the significance level α) suggests that the observed data is unlikely under the null hypothesis. Therefore, we would reject the null hypothesis. Note that "accepting the alternative hypothesis" isn't standard terminology in statistics; instead, we reject or fail to reject hypotheses.

**Question:**
Given a normal distribution with a mean of 80 and a standard deviation of 5, we know that approximately what percent of the values are between 70 and 90?

**Options:**
- ○ 68
- ○ 95
- ○ 99
- ○ 99.7

**Explanation:**
This question involves understanding the properties of a normal distribution. The values 70 and 90 are symmetric around the mean, each one standard deviation (5 units) away from the mean of 80. According to the empirical rule (68-95-99.7 rule) for normal distributions:

- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.

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