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

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

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.

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