 # A Task on Statistical Discussion Topic

Post a total of 3 substantive responses over 2 separate days for full participation. This includes your
initial post and 2 replies to other students.

Respond to the following in a minimum of 175 words:

Let’s try the checkpoint again for discussion since we made progress with the last one:

You find out that the average 10th grade math score, for Section 6 of the local high school, is 87 for the 25 students in the class. The average test score for all 10th grade math students across the state is 85 for 1,800 students. The standard deviation for the state is 3.8.

Q.1:  What z score do you calculate?

Ans: The Z-score is the standardized score which can be used to compare the quantities of different scales and location measures. Since, according to CLT, we have a result that sample mean of reasonable large sample follows standard normal distribution, we use that result to get the comparison for high school math score with all 10-th grade math score.
The Z-score is . Hence, here the z-score would be:
The Z-score means that mean score of 87or more in 25 students is as likely as getting 2.63 or more standard normal distribution.

Q.2: What is the area between the mean and the z score found in Appendix A of the textbook?

Ans: The area between mean and the Z-score is 0.4958
The man of the standard normal distribution is 0. The area under PDF of standard normal
distribution between 0 and 2.63 is 0.4958
The probability of having mean score of 87 or more out of 25 random students under the distribution that true mean is 85 with SD of 3.8 would be 0.5-0.4958 = 0.0042

Q.3: What does this mean about the probability of this test score difference occurring by chance?
Is it less than 0.05?

Ans: Yes. The score lies outside of the region. The probability that mean of 25 students is equal to or greater than 87 is 0.5-0.4958 = 0.0042
Clearly, the obtained probability is smaller than 0.05. Hence, it is very unlikely that the obtained score is just by chance and not out of some systematic bias/cause.