**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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MATLAB: An Introduction with Applications

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Author:Amos Gilat

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A significance test is based on the following idea: Make an assumption about the population (The null hypothesis an assumption that the parameter equals a value). Then test to see if, under the assumption that the null hypothesis is true how likely is the sample that you got? If the sample you got is likely (within the range of normal defined by o or with probability greater then o) then it is possible that both the sample and the null hypothesis is true. If the sample is not likely then both it and the null hypothesis are probably not both true. Since the sample was collected (under the assumption it was collected well) then the null hypothesis is probably not true and we reject the null hypothesis. There are 3 types of significance tests. Left-sided test: Unusual defined by the test statistic being less than the critical value which cuts off or area in the left tail (note these will be negative values, less then means bigger negative) or a p-value less then a, where p-value is the…
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Which of the following decisions do we arrive at if the p-value < a level of significance O Reject the null hypothesis