Question

Independent random samples of students were taken from two high schools, R and S, and the proportion of students who drive to school in each sample was recorded. The difference between the two sample proportions (R minus S) was 0.07. Under the assumption that all conditions for inference were met, a hypothesis test was conducted where the alternative hypothesis was the population proportion of students who drive to school for R was greater than that for S. The p-value of the test was 0.114.
Which of the following is the correct interpretation of the p-value?A. The probability of selecting a student from high school R who drives to school is 0.07, and the probability of selecting a student from high school S who drives to school is 0.114.B. If the proportion of all students who drive to school at R is greater than the proportion who drive to school at S, the probability of observing that difference is 0.114.C. If the proportion of all students who drive to school at R is greater than the proportion who drive to school at S, the probability of observing a sample difference of at least 0.07 is 0.114.D. If the proportions of all students who drive to school are the same for both high schools, the probability of observing a sample difference of at least 0.07 is 0.114.E. If the proportions of all students who drive to school are the same for both high schools, the probability of observing a sample difference of 0.114 is 0.07.

Answer 1

Answer:

Correct option: (D).

Step-by-step explanation:

The hypothesis for testing whether there is a difference between the two population proportions is:

H₀: The population proportion of students who drive to school for R and S is same, i.e. p₁ = p₂.

Hₐ: The population proportion of students who drive to school for R was greater than that for S, i.e. p₁ > p₂.

The difference between the two sample proportion is,

$\hat p_{1}-\hat p_{2}=0.07$

And the p-value of the test is:

p-value = 0.114

The p-value is well defined as the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

The p-value of 0.114 indicates that, assuming the null hypothesis to be true, the probability of obtaining a difference between the two sample proportions of at least 0.07 is 0.114.

The correct option is (D).