Question

Consider the hypothesis test below. ho: p1-p2 <=0

ha: p1-p2>0

The following results are for independent samples taken from the two populations.

Sample 1 |
Sample 2 |

n1 200 | n2 300 |

p-bar 0.24 | p-bar 0.17 |

Use pooled estimator of.

**a.** What is the value of the test statistic (to 2
decimals)?

**b.** What is the -value (to 4 decimals)?

**c.** With , what is your hypothesis testing
conclusion?

- Select your answer -Conclude the difference between the
proportions is greater than 0

Cannot conclude the difference between the proportions is greater than 0

Answer #1

The pooled proportion(P) = ( * n1 + * n2)/(n1 + n2)

= (0.24 * 200 + 0.17 * 300)/(200 + 300)

= 0.198

a) The test statistic z = ()/sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.24 - 0.17)/sqrt(0.198 * (1 - 0.198) * (1/200 + 1/300))

= 1.92

b) P-value = P(Z > 1.92)

= 1 - P(Z < 1.92)

= 1 - 0.9726 = 0.0274

c) At 0.05 significance level, since the P-value is less than the significance level(0.0274 < 0.05), so we should reject the null hypothesis.

Conclude the difference between the proportions is greater than 0.

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Population 2
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400
600
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426
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