Question

Suppose that a one-proportion z-test statistic for a study is calculated to be 2.45. Which of the following is the most appropriate interpretation of this statistic?
Select one:

a. The observed value of the sample proportion is 2.45 times the parameter value assumed by the null hypothesis.
b. The observed value of the sample proportion is 2.45 SDs above the parameter value assumed by the null hypothesis.
c. The observed value of the sample proportion is 2.45 SDs away from the parameter value assumed by the null hypothesis.
d. The study results are statistically significant.

Answer 1

Question:

Suppose that a one-proportion z-test statistic for a study is calculated to be 2.45. Which of the following is the most appropriate interpretation of this statistic?

b. The observed value of the sample proportion is 2.45 SDs above the parameter value assumed by the null hypothesis.

Explanation:

We know that the sampling distribution of sample proportions follows the approximate normal distribution or z-distribution. The Z-score indicate the distance between the standardized value of normal distribution for sample proportion and the parameter value of population proportion. Positive Z score indicate that the statistic is above parameter value and negative Z value indicate that the statistic is below the parameter value. The Z score of 2.45 indicate that the sample proportion is 2.45 SDs above the parameter value assumed by the null hypothesis in this case, because Z value is positive. If Z value is negative, then we would say that sample proportion is below the parameter value.