Question

Two samples are drawn to test the hypothesis, H0: p = 0.5 vs HA: p ≠0.5{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mn>0</mn></msub><mo>:</mo><mo>&#xA0;</mo><mi>p</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>&#xA0;</mo><mi>v</mi><mi>s</mi><mo>&#xA0;</mo><msub><mi>H</mi><mi>A</mi></msub><mo>:</mo><mo>&#xA0;</mo><mi>p</mi><mo>&#xA0;</mo><mo>&#x2260;</mo><mn>0</mn><mo>.</mo><mn>5</mn></math>"}. One sample has size n1=250{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mn>250</mn></math>"} and the other has size n2=125{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>=</mo><mn>125</mn></math>"}. Both samples yield the same sample proportion of 0.4.

Consider the statement:

Both samples will produce the same p-value for the hypothesis test above.

Is this statement always true, sometimes true or never true?

Question 12 options:

	Always true
	Sometimes true
	Never true

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Answer 1

Never true

(since both samples have different sample size, therefore will result in different standard error and different p values)