How do i do this problem

Question

When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right or her left hand, then she asked the therapists to identify the selcted hand by placing their left hand, just under Emily's hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times. Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guess. Do the results suggest that touch therapists are effective?

Find the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion, about the null hypthesis, and final conclusion, that address the original claim.

Answer 1

Step 1:

Among 280 trials, the touch therapists were correct 123 times.

Null hypothesis :

One of these statements must become the null hypothesis , and the other should be the alternate hypothesis.

The null hypothesis contains equality.

So for the above, the null hypothesis H₀ : x = 123.

Step 2:

Alternate hypothesis :

The statement that does not contain equality is the alternative hypothesis.

Number of times the therapists made correct choice may be less than or greater than equal to 123 times.

So for the above, the alternate hypothesis H_a : x < 123 or x > 123.

Solution :

Null hypothesis : H₀ : x = 123.

Alternate hypothesis H_a : x < 123 or x > 123.