RE:7
Now that you are in college you have already taken a number of standardized exams such as the SAT and ACT exams. A Southern California company that creates standardized exams tries to develop multiple choice questions that are not so difficult that those taking the exams are forced to guess at the answers to most questions. Recently, the company received a complaint about one of the problems on an exam. The problem listed five possible answers. If the test takers were forced to guess, the company might expect an even percentage of choices across the five possible answers. That is, each answer is as likely to be a guess as any other answer. To determine if people were actually forced to guess conduct the appropriate test using a significance level of 0.05.
Question for Review
Answer | Times Selected |
---|---|
1 | 358 |
2 | 402 |
3 | 577 |
4 | 403 |
5 | 380 |
As we are testing here whther the frequency is equally likely across the 5 answers , therefore the expected frequency for each answer here is computed as:
= Sum of all Frequency * (1/5)
= (358 + 402 + 577 + 403 + 380) *(1/5)
= 2120*(1/5)
= 385
The chi square test statistic here is computed as:
For n - 1 = 4 degrees of freedom, we get the p-value from the chi square distribution tables here as:
As the p-value here is negligible, therefore it is less than 0.05. Therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that people were actually forced to guess
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