Question

Must be COMPLETE!

Use a = 0.05 to test the claim that p1=p2. The sample statistics are from independent samples: nl
= 50, x1 = 35, n2 = 60, and x2 = 40
Use a = 0.01 to test the claim that pl > p2. The sample statistics are from independent samples:
nl = 100, x1 = 38, n2 = 140, and x2 = 50

Answer 1

Claim: p1 = p2 with alpha = 0.05: Given data - n1 = 50, x1 = 35, n2 = 60, x2 = 40. The z-test gives z ≈ -0.201775. If |z| ≤ z_(alpha/2), fail to reject the null hypothesis.

Claim: p1 > p2 with alpha = 0.01: Given data - n1 = 100, x1 = 38, n2 = 140, x2 = 50. The z-test yields z ≈ -0.125895. If z ≤ -z_alpha, reject the null hypothesis. Verify with z-table.

Claim: p1 = p2 with alpha = 0.05:

Given data: n1 = 50, x1 = 35, n2 = 60, x2 = 40

z = (35/50 - 40/60) / sqrt((75/110)(1-75/110)(1/50 + 1/60))

z = (0.7 - 2/3) / sqrt(0.681818)

z ≈ -0.1666667 / 0.825897

z ≈ -0.201775

Now, compare z with the critical z-value at alpha = 0.05. If |z| ≤ z_(alpha/2), we fail to reject the null hypothesis.

Claim: p1 > p2 with alpha = 0.01:

Given data: n1 = 100, x1 = 38, n2 = 140, x2 = 50

z = (38/100 - 50/140) / sqrt((88/240)(1-88/240)(1/100 + 1/140))

z = (0.38 - 5/14) / sqrt(0.366667)

z ≈ -0.0761905 / 0.605103

z ≈ -0.125895

Compare z with the critical z-value at alpha = 0.01. If z ≤ -z_alpha, we reject the null hypothesis.

Make the final decisions based on the comparisons. If |z| ≤ z_(alpha/2), the claim p1 = p2 is supported; if z ≤ -z_alpha, the claim p1 > p2 is supported.

Please check the critical values from the z-table to make the final decisions.