A forensic psychologist studying the accuracy of a new type of polygraph (lie detector) test instructed a participant ahead of time to lie about some of the questions asked by the polygraph operator. On average, the current polygraph test is 75% accurate, with a standard deviation of 6.5%. With the new machine, the operator correctly identified 83.5% of the false responses. Using the .05 level of significance, is the accuracy of the new polygraph different from the current one? Use the five steps of hypothesis testing.
To determine whether the accuracy of the new polygraph test is different from the current one, we can follow the five steps of hypothesis testing. These steps are:
Step 1: State the hypotheses
Step 2: Formulate an analysis plan
Step 3: Analyze sample data
Step 4: Interpret the results
Step 5: Draw conclusions
Step 1: State the hypotheses
In this case, we want to determine whether the accuracy of the new polygraph test is different from the current one. We can state the null hypothesis (H0) as the accuracy of the new polygraph test is the same as the current one, and the alternative hypothesis (H1) as the accuracy of the new polygraph test is different from the current one.
H0: The accuracy of the new polygraph test = the accuracy of the current polygraph test
H1: The accuracy of the new polygraph test ≠ the accuracy of the current polygraph test
Step 2: Formulate an analysis plan
To test the hypotheses, we will use a two-sample z-test for proportions. This is because we are comparing two samples: the accuracy of the current polygraph test (sample 1) and the accuracy of the new polygraph test (sample 2).
Step 3: Analyze sample data
The information provided states that the current polygraph test has an accuracy of 75% with a standard deviation of 6.5%. The new polygraph test correctly identifies 83.5% of false responses. We can use these percentages to calculate the sample proportions for each test:
Sample proportion for the current polygraph test (p1) = 0.75
Sample proportion for the new polygraph test (p2) = 0.835
Step 4: Interpret the results
We will compare the sample proportions using a two-sample z-test for proportions. The z-test calculates a test statistic based on the difference between two sample proportions and determines the probability (p-value) of obtaining a difference as extreme as the one observed, assuming that the null hypothesis is true.
Step 5: Draw conclusions
We will compare the p-value obtained from the z-test to the predetermined significance level, α = 0.05, to determine whether to reject or fail to reject the null hypothesis.
Note: The calculations for the z-test have been omitted since they require the sample sizes for both tests. Please provide the sample sizes for a complete analysis.
Once you have the sample sizes for both tests, you can calculate the z-score, calculate the p-value, and make a conclusion based on the p-value and the significance level α = 0.05. If you provide the sample sizes, I can help you with the calculation and interpretation of the results.