Hypothesis test (binomial) problem

[coconut62]

Homework Statement

Hester suspected that a die was biased in favour of a four occurring. She decided to carry out a hypothesis test. When she threw the die 15 times, she obtained a four on 6 occasions. Carry out the test, at the 5% level, stating your conclusion clearly.

Homework Equations

None.

The Attempt at a Solution

Ho: p = 1/6
H1: p > 1/6

If Ho is true, then X~B (15, 1/6)
Reject Ho if P (X >= 6) < 5%

P (X >= 6) = 1 - P(X <=5)

= 1- (5/6)^15 - (15C1)(1/6)(5/6)^14 - (15C2)(1/6)^2 (5/6)^13 - (15C3)(1/6)^3 (5/6) ^12 -(15C4)(1/6)^4 (5/6)^11 -(15C5)(1/6)^5 (5/6)^10

=0.0274
=3% (1 s.f.)

Since P (X>=6) < 5%, reject Ho.

The die is biased in favour of 4.

(Answer: no evidence that shows die is biased)

Why am I wrong?

 

[PeroK]

In my view, you're right. The answer must be wrong.

 

[Ray Vickson]

In my view, you're right. The answer must be wrong.

I agree.

 

[coconut62]

Thanks.