Question

The average math score for the class 5 is 23.6. A researcher is interested to check if the score is higher in class 5 that in USA. How many students are needed to ensure that a two-sided test of hypothesis has 80% power to detect a difference in score of 2 marks? If the population standard deviation is 5.7.

Answer 1

To calculate the sample size needed for a study with a certain power, we need to use the formula for power in a two-sample t-test. The formula is:

n = [(Zα/2 + Zβ)^2 * 2 * σ^2] / d^2

where:

- Zα/2 is the critical value from the standard normal distribution for a two-tailed test with the desired level of confidence. If we want a 95% confidence level (typical for this kind of test), Zα/2 would be approximately 1.96.

- Zβ is the critical value corresponding to the desired power. If we want 80% power, Zβ is approximately 0.84.

- σ is the population standard deviation, which is given as 5.7.

- d is the difference we want to detect, which is 2 in this case.

Plugging these values into the formula, we get:

n = [(1.96 + 0.84)^2 * 2 * (5.7)^2] / (2)^2

Now we can calculate this:

n = [7.8 * 2 * 32.49] / 4

n = [504.72] / 4

n = 126.18

The sample size should be a whole number, and it's generally recommended to round up to ensure sufficient power, so we would need a sample size of approximately 127 students in class 5 to have 80% power to detect a difference of 2 marks.

Step-by-step explanation: