College Pass Fail Total 33 17 50 Business Language Arts 32 18 50 Social Science
ID: 3319450 • Letter: C
Question
College Pass Fail Total 33 17 50 Business Language Arts 32 18 50 Social Science 25 25 50 Natural Science 38 12 50 Engineering 43 7 50 Total 171 79 250 Which is the correct interpretation of the p-value when knowing that the test statistic is 16.19 and the p-value = 0.002? The likelihood of obtaining a chi-square statistic of 16.19 or any value: You Answered smaller, if in fact there is a relationship between the two variables in the population, is 0.002. smaller if in fact there is no relationship between the two variables in the population, is 0.002. larger, if in fact there is a relationship between the two variables in the population, is 0.001 Correct Answer larger, if in fact there is no relationship between the two variables in the population, is 0.002Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H0: Two variables in the population are independent.
Ha: Two variables in the population are not independent.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.
Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
2 = [ (Or,c - Er,c)2 / Er,c ]
2 = 16.19
where DF is the degrees of freedom.
We use the Chi-Square Distribution Calculator to find P(2 > 16.2) = 0.002
Interpret results. Since the P-value (0.002) is less than the significance level (0.05), we cannot accept the null hypothesis.
Thus, we conclude that there is a relationship between two variables in the population.