Approximately 50% of the Copper Rings Manufactured by a Company Have Hardness Below 65

ISye 6413 (Spring 2012) : “ASSESS YOUR BACKGROUND” Quiz.

1. Approximately 50% of the copper rings manufactured by a company have hardness below 65 (on Vicker’s scale). With respect to the distribution of hardness of copper rings manufactured by the company, 65 has to be the b a) Arithmetic mean b) Median c) Mode d) Standard Deviation

2. Assuming that the distribution of hardness in the population of copper rings manufactured by the company is normal with mean 65 and standard deviation 1, the approximate percentage of rings that have hardness within 62 and 66 is none of them is right a) 25.35 b) 50.01 c) 75.67 d) 99.73

3. An engineer has to test whether the average hardness of a lot of 1000 manufactured rings is 65. He takes a sample of 20 rings at random from the lot, measures the hardness of each of them and finds that the mean and standard deviation of hardness are 62.5 and 1.2 respectively. The appropriate statistical tool to be used for this problem is c a) Chi-square test b) z-test. c) t-test. d) F-test.

4. After analysis of the data referred to in the previous question, a 95% confidence interval the average hardness in the lot is found to be (55.25, 69.75). Which of the following is a 99% confidence interval for the average hardness of the lot? c a) (57.45, 67.55) b) (57.75, 72.25) c) (53.70, 71.30) d) (56.20, 73.80)

5. It is known that hardenss (H) depends on furnace temperature (T) maintained during the annealing process. The following scatter plot was obtained from 15 pairs of observations on (T,H). Which of the statements given below cannot be correct? d

59 58 57 56 s

s 55 e n 54 d r a 53 H 52 51 50 49 620 630 640 650 660 670 680 Temperature

a) There seems to be a negative linear relationship between temperature and hardness. b) More than 50% of the variation in hardness is explained by furnace temperature. c) Apart from temperature, there are other factors that affect hardness. d) The correlation coefficient between temperature and hardness is 0.8.