Hypothesis Testing Problem – Question 1(In a population, the average IQ…

Question
In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication  has a mean of 140. Did the medication affect intelligence?

Solution Steps
Follow these simple steps in solving this question. Leave a question at the left of this page if you hava any.

Step 1: Set up the null and alternate hypothesis

H₀: medication affects intelligence
H_a: medication does not affect intellignece

(not that the alternate hypothesis is always the opposite of the null hypothesis)

Step 2: Determine the type of test to use
Since the sample size  is 30, we use the z-test. See why we use the z-test when sample size is 30 and above in Parametric Tests in Statistics, When to use which

Step 3: Calculate the tested statistic z using the formula

This formular can also be written like this:

Using the data given in the equation we would have the following:
μ₀ = 100
σ = 15
n = 30
x̄_n = 140 

Plugging the values into the formular we have:

Step 4:  Look up the values of z ( called the critical value) from statistical tables. 
You can access statistical table from here. Statistical Table
From the table: we get a value of 1.96

Step 5: Draw a conclusion
In this case the tested statistic value of z calculated is more than the critical value obtained from statistical tables.

14.606 > 1.96

 Therefore we reject the null hypothesis.
This means, from the question, that the medication administered does not affect intelligence.

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