Question

In a numerosity judgment task, you are presented a number of dots on a computer screen and asked to decide if the number of dots is greater or less than some pre-determined criterion (e.g., is the number of dots greater than or less than 25?). A researcher collected data from 16 subjects, each of which did this task 100 times. The number of incorrect responses (errors) was recorded. The average number of error responses for this sample was 38.4. It is known that the population standard deviation of this task is 10.6. The researcher asked you to check if these subjects participated in the task ‘faithfully’ or randomly. The subjects are expected to do better in the former case (faithful participation) than in the latter case (random guess). If they did the task with random guesses, they would get an average of 57.4 incorrect responses.

You’re going to answer the researcher’s question by doing a hypothesis test. First, calculate the appropriate test statistic. (keep 2 decimal places)

Answer 1

H0:Null Hypothesis: 57.4 (These subjects participated in the task randomly)

HA: Alternative Hypothesis: 57.4 (These subjects participated in the task faithfully)

= 38.4

= 10.6

n = 1600

Take = 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = - 71.698 is less than critical value of Z = - 1.96, the difference is significant. Reject null hypothesis.

Conclusion:
There is sufficient evidence to conclude that these subjects participated in the task faithfully