Question

A company is engaged in the production of feed for farm birds. The company's marketing department has released an advertisement that ensures that the birds that are fed with this product will have a weight gain of at least 130 grams during its first week. The weight gain of these birds is known to follow a normal distribution with variance of 120g2. Given the complaint of fraudulent advertising, filed by some buyers, the Consumer Defender launched an investigation. A sample consisting of 50 birds was used, which was fed with this concentrate during its first week and an average increase of 110 g was recorded.

a) Determine the critical value or values for this hypothesis test (in which the assertion made in the advertisement is statistically analyzed). Use a significance level of 4%.

b) Determine the regions of acceptance and rejection of the hypothesis (statement made in the announcement), using a significance level of 4%.

c) Based on statistical evidence, explain whether the advertisement can be considered fraudulent advertising. Use a confidence level of 96%. All the procedures and calculations that support the conclusion must be presented.

d) Determine the minimum sample size necessary to perform the hypothesis test with a significance level of 2.5% and a power of 91%, if the average weight gain is actually 125 grams.

Answer 1

a)

(b)

c)

d)

The standard deviation is

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