Question

1. A clothing company assumes that the average man is 172 cm with a standard deviation of 30 cm. To test if this is still true, the company orders an analysis of the current height for men. A sample of 50 was taken and the following data (in mm) arouse: x ≈ 1732.49 s 2 s ≈ 4726.66 ss ≈ 68.75

Is it true that the variance has remained the same, at a significance level of 1%?

2. A craft beer factory sells 0.5 L beer bottles. The real content of the bottle X (given in cm3 ) is normal distributed. It is known that the standard deviation is 1.5 cm3 . A consumer protection organization wants to test that, on average, the real average content of the bottles is at least 0.5 L (or 500 cm3 ). The organization took and measure the contents of a sample of 25 bottles and the observed average was x = 499.28.

Perform a test with at a 10% significance for the expected content.

Answer 1

1:

Conclusion: There is no evidence to conclude that the variance has remained the same, at a significance level of 1%

2:

Conclusion: There is no evidence to conclude that  on average, the real average content of the bottles is at least 0.5 L (or 500 cm3 ).