An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Null hypothesis: The means of all three groups are equal: H 0 : μ A = μ B = μ C
Alternative hypothesis: At least one of the group means is different.
Requirements for ANOVA: Independent random samples, approximately normal populations, and equal variances.
Explanation
Analyze the problem We are given data for three groups, A, B, and C, and we want to compare their means using a one-way ANOVA. The problem asks us to state the null and alternative hypotheses and list the requirements for using the ANOVA procedure.
State the null hypothesis The null hypothesis states that the means of all three groups are equal. We can write this as: H 0 : μ A = μ B = μ C
State the alternative hypothesis The alternative hypothesis states that at least one of the group means is different from the others. This does NOT mean that all group means are different, just that there is a significant difference between at least one pair of means. We can write this as: H 1 : At least one group mean is significantly different from the others.
List the requirements for ANOVA The requirements for using the one-way ANOVA procedure are:
The data are independent random samples from each population.
Each population is approximately normally distributed.
The variances of the populations are equal.
Final Answer Therefore, the null hypothesis is that the means of the three groups are equal ( H 0 : μ A = μ B = μ C ), and the alternative hypothesis is that at least one group mean is different. The requirements for ANOVA are independent random samples, approximately normal populations, and equal variances.
Examples
One-way ANOVA is commonly used in medical research to compare the effectiveness of different treatments. For example, researchers might want to compare the average recovery time for patients receiving three different medications. The null hypothesis would be that the average recovery times are the same for all three medications, while the alternative hypothesis would be that at least one medication has a different average recovery time. ANOVA helps determine if the observed differences in recovery times are statistically significant or simply due to random chance.
