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

The power of a statistical test measures the probability of rejecting the null hypothesis when it is false. To calculate the power in this scenario, we need to find the critical value and calculate the z-score for the sample mean.

Step-by-step explanation:

The power of a statistical test measures the probability of rejecting the null hypothesis when it is false, in this case, the probability of concluding that the mean net weight is less than the advertised value of 14 oz when the true mean is actually 13.8 oz.

To calculate the power, we first need to determine the critical value for the test. Since the alternative hypothesis is that the mean is less than 14 oz, the critical value is the value that separates the lower 5% of the distribution under the null hypothesis. We can find this critical value using a z-score table or a statistical software.

Once we have the critical value, we can calculate the z-score for the sample mean. The z-score measures the number of standard deviations the sample mean is away from the population mean under the null hypothesis.

Finally, we can find the power of the test by calculating the probability of obtaining a z-score greater than or equal to the critical value, given the true mean of 13.8 oz.

Answer 2

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