Question

Provide an example of a one sample proportion test in scientific research.

Answer 1

An example of a one sample proportion test:

The IRS stated that last year 25% of tax returns contained arithmetic errors. In a random sample of 500 of this year’s returns, 140 were found to contain errors. Use a hypothesis test to determine whether the proportion of errors in this year’s tax returns is different than 25%.

Solution:

Claim: The proportion of errors in this year’s tax returns is different than 25%

The null and alternative hypothesis is

H0: P = 0.25

H1: P 0.25

Level of significance = 0.05

Sample size = n = 500

Test statistic is

P-value = 2*P(Z >1.55) = 0.1211

P-value > 0.05 we fail to reject null hypothesis.

Conclusion: The proportion of errors in this year’s tax returns is equal to 25%.