A college student takes a standardized test and scores a 163. If the mean is 155 and the standard deviation is 7, what is the student’s percentile rank? (Assume a normal distribution.)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100.
Percentile rank is % ≤ any score.
A researcher is interested in determining whether acupuncture affects pain tolerance. An experiment is performed in which 15 students are randomly chosen from a large pool of university undergraduate volunteers. Each subject serves in two conditions. In both conditions, each subject receives a short-duration electric shock to the pulp of a tooth. The shock intensity is set to produce a moderate level of pain to the unanesthetized subject. After the shock is terminated, each subject rates the perceived level of pain on a scale of 0–10, with 10 being the highest level. In the experimental condition, each subject receives the appropriate acupuncture treatment prior to receiving the shock. The control condition is made as similar to the experimental condition as possible, except a placebo treatment is given instead of acupuncture. The two conditions are run on separate days at the same time of day. The pain ratings in the accompanying table are obtained.
a. What is the alternative hypothesis? Acupuncture treatment and placebo.
b. Once you have generated a hypothesis, the process of hypothesis testing becomes important, comparing your results against the null hypothesis. Assume a nondirectional hypothesis is appropriate.
c. What is the null hypothesis?
d. Using 0.052 tail, what is your conclusion?
One tail represents a positive effect or association; the other, a negative effect.) A one-tailed hypothesis has the statistical advantage of permitting a smaller sample size as compared to that permissible by a two-tailed hypothesis. Unfortunately, one-tailed hypotheses are not always appropriate; in fact, some investigators believe that they should never be used.
e. What error might you be making by your conclusion
f. in part c?
g. To what population does your conclusion apply?
h. Subject Acupuncture Placebo
i. 1 4 6
j. 2 2 5
k. 3 1 5
l. 4 5 3
m. 5 3 6
n. 6 2 4
o. 7 3 7
p. 8 2 6
q. 9 1 8
r. 10 4 3
s. 11 3 7
t. 12 4 8
u. 13 5 3
v. 14 2 5
w. 15 1 4
cognitive, health
To find the student's percentile rank, we can use the cumulative distribution function (CDF) of a normal distribution.
Step 1: Calculate the z-score.
The z-score formula is given by:
Z = (X - μ) / σ
where X is the student's score (163), μ is the mean (155), and σ is the standard deviation (7).
Z = (163 - 155) / 7
Z = 8 / 7
Z ≈ 1.1429
Step 2: Find the percentile rank using the z-score.
Using a standard normal distribution table or a calculator, we can determine the percentile rank associated with the z-score of approximately 1.1429.
Looking up the z-score of 1.14 from the table, we find that the percentile rank is approximately 87.14%.
Therefore, the student's percentile rank is approximately 87.14%.
To find the student's percentile rank, we need to first calculate their z-score using the formula:
z = (X - μ) / σ
Where:
X is the student's score
μ is the mean
σ is the standard deviation
In this case:
X = 163
μ = 155
σ = 7
By substituting the values, we can calculate the z-score:
z = (163 - 155) / 7
z = 8 / 7
z ≈ 1.143
Next, we need to find the percentile associated with the calculated z-score. This can be done using a standard normal distribution table or a statistical software.
Using either method, we find that a z-score of approximately 1.143 corresponds to a percentile rank of approximately 87.94%.
Therefore, the student's percentile rank is approximately 87.94%.