Finding Critical Regions (Binomial Distribution)

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(20, 0.5), H₀ : p=0.5, H₁ : p<0.5

• X ≤ 5

• X ≤ 4

• X ≤ 6

• X ≤ 3

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(30, 0.4), H₀ : p=0.4, H₁ : p<0.4

• X ≤ 5

• X ≤ 6

• X ≤ 7

• X ≤ 8

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(50, 0.2), H₀ : p=0.2, H₁ : p<0.2

• X ≤ 4

• X ≤ 5

• X ≤ 6

• X ≤ 7

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(40, 0.1), H₀ : p=0.1, H₁ : p<0.1

• X = 0

• X ≤ 1

• X ≤ 2

• X ≤ 3

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(105, 0.24), H₀ : p=0.24, H₁ : p<0.24

• X ≤ 15

• X ≤ 16

• X ≤ 17

• X ≤ 18

A one-tailed test at the 10% significance level. The probability has to be under 10%. Find the critical region.

X~B(15, 0.4), H₀ : p=0.4, H₁ : p<0.4

• X ≤ 4

• X ≤ 1

• X ≤ 2

• X ≤ 3

A one-tailed test at the 2% significance level. The probability has to be under 2%. Find the critical region.

X~B(40, 0.25), H₀ : p=0.25, H₁ : p<0.25

• X ≤ 3

• X ≤ 4

• X ≤ 5

• X ≤ 6

A one-tailed test at the 10% significance level. The probability has to be under 10%. Find the critical region.

X~B(17, 0.64), H₀ : p=0.64, H₁ : p<0.64

• X ≤ 6

• X ≤ 7

• X ≤ 8

• X ≤ 9

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(20, 0.5), H₀ : p=0.5, H₁ : p>0.5

• X ≥ 13

• X ≥ 14

• X ≥ 15

• X ≥ 16

A one-tailed test at the 5% significance level. The probability has to be under 5%. Find the critical region.

X~B(30, 0.4), H₀ : p=0.4, H₁ : p>0.4

• X ≥ 15

• X ≥ 16

• X ≥ 17

• X ≥ 18