The Student Room Group

Hypothesis testing

Hi Can anyone help with this question please I'm confused.
Can anyone explain why they did X < or equal to 11, because I did X > or equal to 11. I thought if the coin is biased toward Heads there would be a greater number of Heads in the 18 times tossed.

2. A coin is tossed 18 times and 11 heads come up.
(a) Construct a critical region for a hypothesis test with a 5% significance level, in order
to test the hypothesis that the coin is unbiased as opposed to being biased towards
heads.
(b) Comment on the results.


2. Let p be the probability of obtaining a head.
H0 : p = 0.5
H1 : p > 0.5
Significance level = 5%
(a) Let X be the number of heads obtained.
(Need the lowest possible value of a for which P(X a) < 0.05)
1 P(X a 1) < 0.05
P(X a 1) > 0.95
For B(18, 0.5), P(X 11) = 0.8811
P(X 12) = 0.9519
The lowest possible value of a 1 is 12, so the lowest possible value of a is 13.
The critical region is X 13
Original post by Disha2504
Hi Can anyone help with this question please I'm confused.
Can anyone explain why they did X < or equal to 11, because I did X > or equal to 11. I thought if the coin is biased toward Heads there would be a greater number of Heads in the 18 times tossed.
2. A coin is tossed 18 times and 11 heads come up.
(a) Construct a critical region for a hypothesis test with a 5% significance level, in order
to test the hypothesis that the coin is unbiased as opposed to being biased towards
heads.
(b) Comment on the results.
2. Let p be the probability of obtaining a head.
H0 : p = 0.5
H1 : p > 0.5
Significance level = 5%
(a) Let X be the number of heads obtained.
(Need the lowest possible value of a for which P(X a) < 0.05)
1 P(X a 1) < 0.05
P(X a 1) > 0.95
For B(18, 0.5), P(X 11) = 0.8811
P(X 12) = 0.9519
The lowest possible value of a 1 is 12, so the lowest possible value of a is 13.
The critical region is X 13

I think it's because in a two-tailed test, you need to consider the expected value for X. This can be calculated by the formula np. n is 18, and p is 0.5, which = 9. This is smaller than 11, so X < or equal to 11.
Reply 2
Ohh I see, thank you very much !!

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