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?
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
Ha: 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
x̄n = 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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