An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the degrees of freedom: df = 5 − 1 = 4 .
Determine the p-value from the Chi-square distribution with χ 2 = 10.2344 and df = 4 : p ≈ 0.0367 .
Compare the p-value to the significance level ( α = 0.05 ): 0.0367 < 0.05 .
Reject the null hypothesis: reject .
Explanation
Understand the problem We are given a Chi-square test with a standardized sample score of 10.2344 and 4 degrees of freedom. Our goal is to find the p-value associated with this test statistic and then determine whether to reject or fail to reject the null hypothesis.
Calculate degrees of freedom The degrees of freedom (df) for the Chi-square test is calculated as df = k − 1 , where k is the number of categories. In this case, k = 5 (Vanilla, Chocolate, Butter pecan, Strawberry, Other), so df = 5 − 1 = 4 .
Determine the p-value We need to find the p-value associated with a Chi-square statistic of 10.2344 and 4 degrees of freedom. The p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true. Using a Chi-square distribution table or a calculator, we find that the p-value is approximately 0.0367.
Compare p-value to significance level We compare the p-value to the significance level (alpha). The significance level is not explicitly given, but we can assume a standard value of 0.05.
Make a decision If the p-value is less than or equal to the significance level (alpha), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis. In this case, the p-value (0.0367) is less than the significance level (0.05), so we reject the null hypothesis.
Conclusion Since the p-value (0.0367) is less than the significance level (0.05), we reject the null hypothesis.
Examples
Chi-square tests are commonly used in marketing to determine if there is a significant association between different categorical variables, such as customer demographics and product preferences. For example, a company might use a Chi-square test to determine if there is a relationship between a customer's age group and their preferred flavor of ice cream. This information can then be used to tailor marketing campaigns to specific age groups, increasing the effectiveness of the campaigns and improving sales.
In 30 seconds, an electric device delivering a current of 15.0 A allows approximately 2.81 x 10^21 electrons to flow through it. This is calculated using the relationship between current, charge, and time. The formula used is Q = I × t, which leads to the total charge being divided by the charge of a single electron.
;
