Question

We have five samples of data: sample A with 30 successes of 50 cases, sample B with 600 successes of 1000 cases, sample C with 3000 successes of 5000 cases, sample D with 60 successes of 100 cases and sample E with 300 successes of 500 cases. We want to test if the proportion of successes is greater than 0.5. Which sample gives the strongest evidence for the alternative hypothesis

Answer 1

C with 3000 successes of 5000 cases

Explanation:

In test statistics the number of samples goes a long way in determining the result of a test.

Using the z score formula

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size

po = Null hypothesized value

p^ = Observed proportion

Therefore the z score is directly proportional to the square root of the sample size.

z ∝ √n

The higher the sample size, the higher the z score, the higher the evidence of confirming the alternative hypothesis.

Since the all have the same proportion (0.6), and options c has the highest sample size (5000 cases), it will give the strongest evidence for the alternative hypothesis