(a). Mean strength of a particular brand of thread is 9.72N with standard deviation of 1.40N. Recently, a sample of 36 pieces showed a mean breaking strength of 8.93N. Can we conclude at =0.01 that the thread has become inferior?

(b). The recommended limit of iron and manganese in water is 0.30 ppm (i.e, it should not exceed 0.30 ppm). A textile company has sued the State Water Supply Corporation because of some damage in her production process caused by excessive iron and manganese content in water supply. An expert sanitary Engineer, called to supply a technical evidence, sampled from the water supply and discovered that the mean and standard deviation are 0.35 and 0.08 respectively for 100 samples. At 1% level of significance, should the water corporation be convicted?