Below is a hypothesis test set up

Question

Below is a hypothesis test set up by a student who recently took introductory statistics:

 

Ho: x = 5
Ha: x ≠ 5

 

The sample mean of 100 cases used to implement the hypothesis test is x = 4.2
Which of the following statements is accurate?

 

1. This is a one-sided hypothesis test.
2. There is an error in how these hypotheses were constructed.
3. It would be reasonable to swap “<” for “≠” in the alternative hypothesis.

(a) 1 only
(b) 2 only
(c) 3 only
(d) 1 and 2
(e) 1 and 3
(f) 2 and 3

Answer 1

1 is clearly false since H_a could be true if x < 5 or x > 5 so it is a two-sided test 

2 is also false 

3 is true since that would make it a one-sided test