Construct a 95% confidence interval for 'P1-P2'.

The sample statistics listed below are from independent samples. x1 = 35 x2 = 40 / / n1=50 n2=60

Answer: interval proportion = - 0.144, 0.204

Step-by-step explanation: from the question.

X1 = 35, n1 = 50, x2 = 40, n2 = 60

P1=x1/n1=35/50 = 7/10 = 0.7,

1-p1 = 1 - 0.7 = 0.3

P2 = x2/n2 = 40/60 = 2/3 = 0.67

1 - p2 = 1 - 0.67 = 0.33

95% confidence interval for population proportion is given as

p1-p2 + Zα/2 * √{p1 (1-p1) / n1 + p2 (1-p2) / n2} ... This is the upper limit

p1-p2 - Zα/2 * √{p1 (1-p1) / n1 + p2 (1-p2) / n2} ... This is the lower limit

p1 = first sample proportion = 0.7

p2 = second sample proportion = 0.67

n1 = first sample size = 50

n2 = second sample size = 60

Zα/2 = z score for a two tailed test at 5% level of significance = 1.96.

Upper limit

(0.7 - 0.67) + 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 + 1.96 {√ (0.0042 + 0.003685) }

0.03 + 1.96 √0.007885

0.03 + 1.96 (0.08879)

0.03 + 0.174

= 0.204.

Upper limit

(0.7 - 0.67) + 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 + 1.96 {√ (0.0042 + 0.003685) }

0.03 + 1.96 √0.007885

0.03 + 1.96 (0.08879)

0.03 + 0.174

= 0.204.

Lower limit.

Upper limit

(0.7 - 0.67) + 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 + 1.96 {√ (0.0042 + 0.003685) }

0.03 + 1.96 √0.007885

0.03 + 1.96 (0.08879)

0.03 + 0.174

= 0.204.

Upper limit

(0.7 - 0.67) + 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 + 1.96 {√ (0.0042 + 0.003685) }

0.03 + 1.96 √0.007885

0.03 + 1.96 (0.08879)

0.03 + 0.174

= 0.204.

Upper limit

(0.7 - 0.67) + 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 + 1.96 {√ (0.0042 + 0.003685) }

0.03 + 1.96 √0.007885

0.03 + 1.96 (0.08879)

0.03 + 0.174

= 0.204.

Lower limit

(0.7-0.67) - 1.96 * {√ (0.7*0.3/50 + 0.67*0.33/60) }

0.03 - 1.96 {√ (0.0042 + 0.003685) }

0.03 - 1.96 √0.007885

0.03 - 1.96 (0.08879)

0.03 - 0.174

= - 0.144

interval proportion = - 0.144, 0.204