Question

QUESTION 1 :

Fertilizer is sold in bags. Weights of fertilizer in bags are normally distributed. The actual mean weight of a bag is found to be 20 kg. 27 bags were randomly selected, piled on a pallet and weighted. Those 27 bags had a mean of 20.87 kg and a standard deviation of 0.34251 kg. If the variance of weight is less than 0.1225 no adjustment is made. Otherwise, the machine is adjusted.

1. Calculate a 99% confidence interval on the variance of weights. Interpret your result.

2. Do you think that the machine needs adjustment? Use a = 0.05.
   1. Formulate the hypotheses.
   2. Write test statistics and calculate its value.
   3. Find critical value and write rejection criteria.
   4. Write your conclusion.
   5. Calculate appropriate confidence interval to test the claim. State your result and draw your conclusion about the hypothesis.

Answer 1

The variance of the sample is

a:

b:

(v)

The population SD is

Since confidence interval contains 0.35 so there is no evidence that the variance of weight is less than 0.1225.