Which of the following is the best example of something that is statistically si

Question

Which of the following is the best example of something that is statistically significant but NOT practically significant?

a) A hypothesis test determines that the proportion of drivers not wearing a seatbelt has decreased from 4.0% to 3.5%, with a p-value of 0.005.

b) A hypothesis test determines that the mean age of undergraduate students at Georgia universities has increased from 21.12 years to 21.13 years, with a p-value of 0.005.

c) A hypothesis test determines that the proportion of drivers not wearing a seatbelt has decreased from 4.0% to 3.5%, with a p-value of 0.5.

d) A hypothesis test determines that the mean age of undergraduate students at Georgia universities has increased from 21.12 years to 21.13 years, with a p-value of 0.5.

Explanation / Answer

Option (B) is correct.

(C) and (D) are not statistically significant results because p-value is greater than usual significance level of 0.05. Hence we fail to reject null hypothesis in these cases, this means results are not statistically significant.

(A) is the genuine case where we reject null hypothesis and accept the alternate hypothesis. This is statistically significant. This also looks practically significant as we re testing the propotion difference of 0.005. Though it is very small but being proportion we can consider it. (This can be argued)

(B) is definitely not practical significant because here we are testing the difference in the mean of 0.01 years. This test will always results into rejection of null hypothesis.

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