**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**

**H _{0}:** medication affects intelligence

**H**: medication does not affect intellignece

_{a}(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:

μ_{0} = 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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it’s wrong. Ho and Ha have to swap.

H0:μ=100

Ha:μ≠100

Calculation is OK

Therefore we reject the null hypothesis.

This means that the medication administered affect intelligence.