John Halikias, plant manager at HOU Vacuum Products, located in Patras, Ahaia, applies statistical thinking in his workplace. As a major supplier to automobile manufacturers, HOU wants to be sure that the leak rate (in cubic centimetres per second) of transmission oil coolers (TOCs) meets the established specification limits. A random sample of 50 TOCs is tested, and the leak rates are recorded in the attached file.

1. Estimate with 95% confidence the mean leak rate for this particular product.

2. Chyundai Motors, one of the largest customers of HOU Vacuum Products, requires that the leak rate of transmission oil coolers should not exceed the value of 0.05 cubic centimetres per second. 

a. State the null and the alternative Hypotheses

b. Test the hypothesis at α = 5%

c. On the basis of your results, are Chyundai Motors requirements satisfied?