If Dr. Robinson rejects the null hypothesis after observing a test statistic which exceeds the critical value at the .05, there is
What are your choices?
a 5% probability that the null hypothesis is true?
Alpha error = 5%?
strong evidence to support the alternative hypothesis.
To understand this statement, let's break it down into a few key concepts:
1. Hypothesis testing: Hypothesis testing is a statistical procedure used to make inferences or draw conclusions about a population based on a sample. It involves formulating two competing hypotheses: a null hypothesis (H0) and an alternative hypothesis (Ha).
2. Null hypothesis (H0): The null hypothesis represents the status quo or the default assumption. It is typically formulated as an assertion that there is no relationship or difference between variables. In the context of Dr. Robinson's situation, the null hypothesis would state that there is no effect or relationship between the variables being tested.
3. Test statistic: In hypothesis testing, a test statistic is a numerical value calculated from the sample data that measures how well the data aligns with the null hypothesis. It is used to assess whether the observed results are unusual enough to reject the null hypothesis.
4. Critical value: The critical value is a threshold set to determine whether to reject or fail to reject the null hypothesis. It is based on the desired level of significance, often denoted as alpha (α). In this case, the critical value is set at 0.05, which means that there is a 5% chance of incorrectly rejecting the null hypothesis.
Now, let's put it all together:
If Dr. Robinson rejects the null hypothesis after observing a test statistic that exceeds the critical value at the 0.05 level of significance, it means that the observed results are statistically significant. The test statistic indicates that the sample data strongly supports the alternative hypothesis, suggesting that there may indeed be a relationship or effect between the variables being tested.
By comparing the calculated test statistic with the critical value, Dr. Robinson can make an informed decision regarding whether to reject the null hypothesis. In this case, if the test statistic exceeds the critical value, it provides strong evidence to confidently reject the null hypothesis in favor of the alternative hypothesis.