Test the hypothesis that eating fish oil makes one smarter, a random sample of 12 persons take a fish oil supplement for one year and then given an IQ test. The results are: population average = 100, sample average = 106, standard deviation = 8.8 and level of significance = 0.05
To test the hypothesis that eating fish oil makes one smarter, we can perform a hypothesis test using the given information.
Null Hypothesis (H₀): Eating fish oil does not make a person smarter. The population average IQ is not significantly different from the sample average IQ.
Alternative Hypothesis (H₁): Eating fish oil makes a person smarter. The population average IQ is significantly higher than the sample average IQ.
Using the sample data, we will calculate the test statistic and compare it to the critical value to make a decision.
1. Test Statistic:
The test statistic for this hypothesis test is the z-score, which measures how many standard deviations the sample average is from the population average.
z = (sample average - population average) / (standard deviation / sqrt(sample size))
z = (106 - 100) / (8.8 / sqrt(12))
z = 6 / (8.8 / 3.464)
z = 6 / 2.536
z = 2.366
2. Critical Value:
With a level of significance (α) of 0.05 (5%), we can find the critical value from a standard normal distribution table or calculator. The critical value for a one-tailed test (since our alternative hypothesis states that the population average is significantly higher) at α = 0.05 is approximately 1.645.
3. Decision:
Since the calculated test statistic (2.366) is greater than the critical value (1.645), we reject the null hypothesis.
4. Conclusion:
Based on the sample data and hypothesis test, there is sufficient evidence to support the claim that eating fish oil makes a person smarter. The population average IQ is significantly higher than the sample average IQ, indicating that fish oil supplementation may have a positive effect on intelligence.