Question

The population IQ score was collected from a national-wide test. The mean population IQ score is 101 and with a stand deviation of 15. The data of original population follows the normal distribution.

Use the Z-score table provided to answer the following questions:

(1) What is the Z score for IQ score = 95? Answer:  (Please report your answer to 3 decimal places.)

(2) What is the Z score for IQ score = 110? Answer:  (Please report your answer to 3 decimal places.)

(3) What is the probability of students with IQ scores between 95 and 110? (Hint: Pr (95 <IQ < 110))

Answer:  (Please report your answer to 4 decimal places.)

Note: This table gives us the probability that Z is smaller than a given negative number (See the diagram below). Probabilities corresponding to positive Z values are not included in this table. However, recall the all normal distribution are symmetric around their means and the standard normal distribution is symmetric around µ = 0. This means that Pr (Z< -number) = Pr (Z > number).

For example, Pr (Z< -3.6) = Pr (Z > 3.6)

A principle at a middle school claims that the students in his school are above average intelligence. A random sample of twenty students’ IQ scores have a mean score of 109.5. Is there sufficient evidence to support the principal’s claim?

(4) The null hypothesis is: Answer:

       a. The sampled data is drawn from the original population: µ₀ =101

       b. The sampled data has average IQ scores larger than 101: µ₀ > 101

       c. The sampled data has average IQ scores smaller than 101: µ₀ < 101

(5) Sample size n =  (Whole number only)

(6) Z value =  (Please report your answer to 3 decimal places.)

(7) The significance level is set as α = 0.05. Use Z-score table provided to report the exact P value of your z score (Please report your answer to 4 decimal places.)

Answer:

(8) Compare the calculated P value to the one at significance level α = 0.05, do you reject or fail to reject the null hypothesis?  (Please answer reject or fail to reject)

(9) Is the principal’s claim justified? Answer:  (answer Yes or No)

Answer 1

Hope this will help you. Thank you :)