Prema Kumari is trying to test the innovativeness in different industries. She has developed an Industrial Innovative Index (popularly known as 3I), which is based on weighted average of 12 different components obtained through a survey instrument. She obtained the data from 12 units from software industry and 10 units in automobile industry. She calculated 3I for each of the units and then summarized the same for the respective industry. The summarized data is presented below

3. If Prema Kumari calculates separate confidence intervals of the same confidence level for the population means of both industries (S and A), then ______

A. The width of the interval for software industry will always be smaller than that of the automobile industry

B. The width of the interval for software industry will always be greater than that of the automobile industry

C. The width of the interval for software industry will always be equal to that of the automobile industry, since the confidence levels are same

D. Whether the width of the interval for software industry will be smaller or greater than that of the automobile industry will depend on the confidence level

4. Prema Kumari tested a hypothesis that there is no difference in the 3I scores between the population means of both industries (H0: S = A), assuming that ?1 = ?2. She also decided that ? = 0.01. The result of the test indicates that ________

A. The null hypothesis is rejected because p value is less than 0.01

B. The null hypothesis is rejected because p value is between 0.01 and 0.05

C. She failed to reject the null hypothesis because the p value is greater than 0.05

D. She failed to reject the null hypothesis because the p value is less than 0.01

sample Sample Standard mean Deviation Software 248 52 Automobile 317 50