Question

The label on a package of cords claims that the breaking strength of a cord is 3.5 pounds, but a hardware store owner believes the real value is less. She plans to test 36 such cords: if their mean breaking strength is less than 3.25 pounds, she will reject the claim on the label. If the standard deviation for the breaking strengths of all such cords is 0.9 pounds, what is the probability of mistakenly rejecting a true claim?​

Answer 1

0.048

Step-by-step explanation:

H0: μ = 3.5 ;

HA : μ < 3.5 ;

m = 3.25 ;

sample size, n = 36 ;

Standard deviation = 0.9

Probability of mistakenly rejecting a true claim:

Zscore = (m - μ) / s.e

s.e = standard error = standard deviation / sqrt(n)

s.e = 0.9 / sqrt(n) = 0.9 / sqrt(36) = 0.9 / 6 = 0.15

P( Z < (3.25 - 3.50) / 0.15)

P(Z < - 1.667) = 0.048