Question

Consider the following results for independent samples taken from two populations.

Sample 1 |
Sample 2 |

n_{1} = 500 |
n_{2}= 200 |

p_{1}= 0.45 |
p_{2}= 0.34 |

**a.** What is the point estimate of the difference
between the two population proportions (to 2 decimals)?

**b.** Develop a 90% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use *z*-table.

to

**c.** Develop a 95% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use *z*-table.

to

Answer #1

solution:-

a.point estimate

**=> p1 - p2 = 0.45 - 0.34 = 0.11**

b.90% confidence for z is 1.645

confidence interval formula

=> (p1 - p2) +/- z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

=> 0.11 +/- 1.645 * sqrt(0.45(1-0.45)/500 +
0.34(1-0.34)/200)

=> 0.11 +/- 0.0661

**=> (0.0439 , 0.1761)**

c.95% confidence for z is 1.96

confidence interval formula

=> (p1 - p2) +/- z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

=> 0.11 +/- 1.96 * sqrt(0.45(1-0.45)/500 +
0.34(1-0.34)/200)

=> 0.11 +/- 0.0788

**=> (0.0312 , 0.1888)**

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Use z-table.
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