5. A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the head of the pin. Measurements on the Rockwell hardness were made for each of the 12, yielding an average...

Extracted text: 5. A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the head of the pin. Measurements on the Rockwell hardness were made for each of the 12, yielding an average value of 48.50 with a sample variance of 2.25. Assuming the measurements to be normally distributed, construct a 90% confidence interval for the mean Rockwell hardness. 6. A machine is being used for packaging popcom. It is known that the standard deviation of the net weight of all popcom is 0.78g. A quality engineer selects a sample of 12 consecutive popcorm packages filled during the production process and gets a mean net weight of 15.4g. Construct a 98.2% confidence interval for the true net weight for al such popcom packages. 7. A researcher wants to estimate the average weight of all mice after they were given some nutritious herb extract. From experience it is known that the standard deviation of all mice is 123g. A random „sample of 10 mice is taken and the data (in grams) below is obtained: 39.8 43.3 45.1 42.3 44.5 41.4 40.6 40.2 43.9 45.3 (a) Find a point estimate for the true mean weight of all such mice. (b) Construct a 96.5% confidence interval for the true imean weight of all such mice. 8. A study on hearing impairment among workers in a construction site bas been done. A random sample of 33 workers has been tested and the results are as follows: