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7. Two different rifles are tested at the shooting range. 190 shots were fired from the first rifle and the target was hit 158 times. 140 shots were fired from the second rifle, with 107 hits. Construct a 95% confidence interval for the difference in the two rifles accuracy. Use the z-values rounded to two decimal places to obtain the answers.

Respuesta :

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Answer:

(-0.02 ; 0.16)

Step-by-step explanation:

n1 = 190 ; n2 = 140

hits 1, x1 = 158 ; hits 2, x2 = 107

P1 = x1/n1 = 158 / 190 = 0.8316

P2 = x2/n2 = 107 / 140 = 0.7643

Zcritical at 95% = 1.96

Confidence interval :

(P1 - P2) ± Zcritical * standard error

Standard Error = sqrt[(p1(1-p1))/n1 + (p2(1-p2))/n2]

S.E = sqrt((0.8316(0.1684))/190 + (0.7643(0.2357))/140) = 0.0449868

(0.8316 - 0.7643) ± (1.96 * 0.0449868)

0.0673 ± 0.0881741

Lower boundary = 0.0673 - 0.0881741 = −0.020874

Upper boundary = 0.0673 - 0.0881741 = 0.1554741

(-0.02 ; 0.16)

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