Question

bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. net weights actually vary slightly from bag to bag. assume net weights are normally distributed. a representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses h0: \mu = 14, ha: \mu < 14. to do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. he finds a sample mean of 13.88 oz with a standard deviation of s = 0.24 oz. assume the standard deviation for the distribution of actual net weights for bags of tortilla chips of this brand is \sigma = 0.25. at the 5% significance level, what is the power of our test when, in fact, \mu = 13.8 oz?

Answer 1

Answer:

Power of test  = 0.1

Step-by-step explanation:

The value of power of function is called Power of test. The Power function of testing hypothesis would be defined as the probability of rejecting H₀ while H₀ is false.

Power of test is denoted as 1-β which is expressed as P(x ∈ W I Ha)

in our case P(x ≥ 0, Hₐ)

Under Hₐ μ = 13.8 then we know that, Z = {x - E(x)}/(σ/√n)

where x = 13.88, σ, 0.25, n = 16, Hₐ μ= 13.8 = E(x) [x.....Normal distribution]

Z = (13.88 - 13.8)/((0.25)/(√16)) = 1.28

Therefore 1-β = P(z ≥ 1.28) = 0.5 - 0.3997 = 0.1, (from z table values)

hence, the power of our test when μ = 13.8 is 0.1