Question

The calibration of a scale is to be checked by weighing a 13 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with

σ = 0.200 kg.

Let μ denote the true average weight reading on the scale.

(a)

What hypotheses should be tested?

H₀: μ ≠ 13
H_a: μ = 13H₀: μ = 13
H_a: μ > 13    H₀: μ ≠ 13
H_a: μ < 13H₀: μ = 13
H_a: μ ≠ 13H₀: μ = 13
H_a: μ < 13

(b)

With the sample mean itself as the test statistic, what is the P-value when

x = 12.85?

(Round your answer to four decimal places.)

What would you conclude at significance level 0.01?

Conclude that the true mean measured weight differs from 13 kg.Conclude that the true mean measured weight is the same as 13 kg.    

(c)

For a test with

α = 0.01,

what is the probability that recalibration is judged unnecessary when in fact

μ = 13.1?

(Round your answer to four decimal places.)For a test with

α = 0.01,

what is the probability that recalibration is judged unnecessary when in fact

μ = 12.9?

(Round your answer to four decimal places.)

Answer 1

a)

H₀: μ = 13
H_a: μ ≠ 13

b)

for above test statistic z =(12.85-13)*sqrt(25)/0.2= -3.75

for above p value =0.0002

c)

probability that recalibration is judged unnecessary when in fact μ = 13.1 is =0.5319

probability that recalibration is judged unnecessary when in fact μ = 12.9 is =0.5319