Question

10) A study of 45 bolts of carpet showed that their average length was 80.2 yards. The standard deviation of the population is 4.6 yards. Which of the following is the 80% confidence interval for the mean length per bolt of carpet? A) 78.4 < μ < 82.0 C) 79.6 < μ < 80.8 B) 79.8u 80.6 D) 79.3 <u < 81.1

Answer 1

Solution :

Given that,

$\bar x$ = 80.2

$\sigma$ = 4.6

n = 45

At 80% confidence level the z is ,

$\alpha$  = 1 - 80% = 1 - 0.80 = 0.20

$\alpha$ / 2 = 0.20 / 2 = 0.10

Z_$\alpha$/2 = Z_0.10 = 1.282

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 1.282 * (4.36 / $\sqrt$45)

= 0.83

At 80% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

80.2 - 0.83 < $\mu$ < 80.2 + 0.83

79.3< $\mu$ < 81.1

(79.3668 , 81.0332)