A random sample was taken from the normal IQ population, which has μ = 100 and σ = 15.
ALL INFORMATION IS GIVEN:
We gave a random sample of 25 undergrad students (n = 25) a new study pattern to see if it increases their IQ score. The samples mean IQ score is 112. The alpha used is (α) .05.
Does the new study pattern increase the undergraduates IQ score? Follow all the steps to calculate and answer the question above!!!
Step 1 - State hypotheses:
Step 2 - Find the critical regions and draw the distribution:
Step 3 – Compute z statistic (also plot distribution):
Step 4 – Make a decision:
Step 1 - State hypotheses:
Null hypothesis (H0): The new study pattern does not increase the undergraduates' IQ score.
Alternate hypothesis (Ha): The new study pattern increases the undergraduates' IQ score.
Step 2 - Find the critical regions and draw the distribution:
Since the population standard deviation (σ) is known, we will use the z-test for hypothesis testing.
The critical region is determined based on the significance level (alpha), which is given as 0.05.
For a two-tailed test, we divide the alpha by 2 to find the critical value for each tail. In this case, the critical values are z = -1.96 (left tail) and z = 1.96 (right tail).
Next, we plot the normal distribution with the mean (μ) of 100 and standard deviation (σ) of 15. We mark the critical values on the distribution.
Step 3 – Compute z statistic (also plot distribution):
To compute the z statistic, we use the formula:
z = (sample mean - population mean) / (population standard deviation / √sample size)
In this case:
Sample mean (x̄) = 112
Population mean (μ) = 100
Population standard deviation (σ) = 15
Sample size (n) = 25
Plugging in the values, we get:
z = (112 - 100) / (15 / √25)
z = 12 / (15 / 5)
z = 12 / 3
z = 4
We plot the z value of 4 on the distribution.
Step 4 - Make a decision:
In this step, we compare the computed z statistic with the critical values to make a decision.
Since the computed z value of 4 falls in the right-tail critical region (beyond z = 1.96), we reject the null hypothesis.
Therefore, we conclude that the new study pattern increases the undergraduates' IQ score.