Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis latex: h_0=\mu=12h0=μ=12 against latex: h_1=\mu> 12h1=μ> 12 using a random sample of specimens. calculate the p-value if the observed statistic is. round your final answer to five decimal places

Answer

given,

mean = 12 Kg

standard deviation = 0.5 Kg

assume the observed statistic is = 11.1

 now,

assuming the number of sample = 4

n = 4

Hypothesis test:

H₀ : μ≥ 12

Ha : μ < 12

now,

significant level α = 0.05

     z* = -3.60

Test statistics, Z* = -3.60

P-value

P(Z<-3.60) = 0.002 (from z- table)

P- value = 0.002

now,

reject the value of H₀ when P-value < α

    0.002 < 0.05

since, it is less P-value < α , we have to reject the null hypothesis

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step-by-step explanation: