Question

A study considers whether the mean score of a college entrance exam for students in 2019 (Group 1) was higher than the mean score in 2018 (Group 2). A random sample of 25 students who took the exam in 2019 and a random sample of 25 students who took the exam in 2018 were selected. Assume α=0.1. If the p-value is 0.34, which is the following is an accurate interpretation?

(a) At α=10%, there is sufficient evidence to indicate that the mean score of a college entrance exam for students in 2019 is higher than the mean score in 2018.

(b) At α=10%, there is not sufficient evidence to indicate that the mean score of a college entrance exam for students in 2019 is higher than the mean score in 2018.

(c) At α=10%, there is sufficient evidence to indicate that the mean score of a college entrance exam for students in 2019 is different from the mean score in 2018.

(d) At α=10%, there is not sufficient evidence to indicate that the mean score of a college entrance exam for students in 2019 is different from the mean score in 2018.

Answer 1

A study considers whether the mean score of a college entrance exam for students in 2019 (Group 1) was higher than the mean score in 2018 (Group 2).

Therefore, the null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 > μ2

p-value for this test is 0.34

Since, p-value is greater than α = 0.1, we fail to reject the null hypothesis.

Interpretation of this result is :

At α=10%, there is not sufficient evidence to indicate that the mean score of a college entrance exam for students in 2019 is higher than the mean score in 2018.