Please find the attachment. It's basically Management science problems.

Test of Mean with Known 9. A random sample of 100 students from the current year's batch gives the mean CGPA as 3.55 and variance 0.04. Can we say that this is same as the mean CGPA of the previous batch which was 3.5? 10. It has been found from experience that the mean breaking strength of a brand of thread is 500 gms with a s.d. of 40 gms. From the supplies, received during the last month, a sample of 16 pieces of thread was tested which showed a mean strength of 450gms. Can we conclude that the thread supplied is inferior? 11. A telephone company's records indicate that individual customers pay on an average Rs 155 per month for long-distance telephone calls with s.d. Rs 45. A random sample of 40 customers' bills during a given month produced a sample mean of 160 for longdistance calls. At 5% significance, can we say that the company's records indicate laser mean than the actual, i.e., actual mean is more than 155 mts? Test of Mean with Unknown 12. A sample size of 10 drawn from a normal population has mean as 31 and variance as 2.25. Is it reasonable to assume that the mean of the population is 30? Assume = 0.01. 13. A car manufacturer claims that its new car gives a mileage of at least 10 kms. Per litre (kmpl) of petrol. A sample of 10 cars is taken and their mileage recorded as follows (in kmpl): 11.2, 10.7, 11.3, 11.0, 10.8, 10.7, 10.6, 10.6, 10.7, 10.4 Is there any statistical evidence to support the claim of the manufacturer about the mileage of its car? 14. The mean nicotine content of a brand of cigarette is 20.0 mgs. A new process is proposed to lower the nicotine content without affecting the flavour. To test the new process, 16 cigarettes are selected at random from the week's output from the test plant. The sample mean nicotine content is found to be 18.5 mg. If the s.d. of nicotine contents is calculated to be 2 mgs, is the claim of the new process justified? Use 5% level of significance. Test of Proportion 15. A cable TV operator claims that 50% of homes in a city have opted for his services. Before sponsoring advertisements on the local cable channel, a company conducted a survey and found that 280 out of 600 homes were cable TV services from the operator. On the basis of this data can we accept the claim of the cable TV operator? 16. In a departmental store, 380 customers out of a random sample of 800 customers were found to be using Visa credit card. Discuss whether this information supports the view that the majority of customers of the store are using cards other than visa. 17. A manufacturer of LCD TV claims that it is becoming quite popular and that about 5% homes are having LCD TV. However a dealer of conventional TVs claims that the percentage of homes with LCD TV is less than 5%. A sample of 400 households is surveyed and it is found that only 18 households have LCD TV. Test at 1 % level of significance whether the claim of the company is tenable. Test of Two Populations Equality of Two Means 1 = 2 = known 18. An automobile company is interested in testing the mileage given by one of the car brands in two different cities, Kolkata and Delhi. The company surveyed 100 car owners in Kolkata and found that the average mileage is 12 kmpl. Out of 150 car owners in Delhi, the mileage averaged to 12.5 kmpl. The s.d. for mileage of this brand of car is known to be 0.9 km. Can we state that these two cities give different mileage. Assume 5% level of significance. 1 = 2 = but unknown 19. A car manufacturer is procuring car batteries from two companies. For testing whether the two brands of batteries say A and B had the same life, the manufacturer collected data about the lives of both brands of batteries from 20 car owners - 10 using A brand and 10 using B brand. The live were reported as follows: Battery brand A 50 61 54 60 52 58 55 56 54 53 Battery brand B 65 57 60 55 58 59 62 67 56 61 Test at 5% level of significance whether both the brands of batteries have the same life? 1 2 and unequal 20. With the purpose of comparing the caffeine content of two brands of coffee, the caffeine contents of 50 mg jars of both the brands are measured. A random sample of ten jars of brand 1 and another random sample of 15 jars of brand 2 are taken. The mean caffeine content obtained from brand 1 is 9.2 mg per 50 gm jar with a s.d. of 0.52 mg and brand 2 id 8.1 mg per 50 gm jar with a s.d of 0.67 mg. Assuming that the two populations of caffeine contents of coffee of two brands are normally distributed with unequal variances, test at 5% level whether the caffeine contents are equal for the coffee of two brands. Paired t test 21. As per ET-TNS Consumer Confidence Survey, published, the consumer confidence indices for some of the cities changed from Dec 2014 to Dec 2015 as follows. City Dec 2014 Dec 2015 Delhi 106 83 Jaipur 117 142 Mumbai 112 126 Ahmedabad 123 108 Kolkata 83 84 Bhubaneswar 137 144 Bangalore 137 138 Kochi 113 134 Is the difference significant? 22. Five salesmen were imparted a one week specialized training for improving their selling skills. The following data was recorded during the month preceding the training and the month after the training relating to their sales per month. Before (Rs in Lakh) 5 6.2 5.4 4.5 5.6 After (Rs in Lakh) 5.5 7 5.6 5.5 6.6 Can we conclude that the training has made any significant impact? Testing of equality of two means and Confidence interval for the difference between the two means 23. According to an automobile agency, average lives of two premium brands A and B of car tyres are 45000 km and 42000 kms. Suppose that these mean lives are based on random samples of 50 brand A and 40 brand B and the s.d. of these two brands were 3000 kms and 2000 kms respectively. - What is the point estimate of the difference in mean lives of two brands of tyres (m1-m2)? - Construct a 95% confidence interval for difference between two means. - Test whether the mean lives of the two brands of tyres are equal? Testing of equality of two proportions and Confidence interval for the difference between the two proportions 24. A soap manufacturing company wanted to estimate the difference between the proportions of loyal users of its soap in urban and rural areas. In a sample of 1200 users from urban areas, 300 users were found to be loyal users and in the sample of 1500 from rural areas, 300 were found to be loyal. Let p1 and p2 be the proportions of loyal users in urban and rural areas respectively. 1.What is the point estimate of the difference of proportions of loyal users of the soap in urban and rural areas i.e., (p1-p2). Construct a 95% confidence interval for the proportion of the same. 2.At 1% significance level, can we conclude that the proportion of loyal users of the soap in urban areas is higher than the proportion of loyal users in rural areas? Equality of Two Proportions 25. A firm wanted to choose a popular actor to be the brand ambassador for the firm's product. However, before taking the final decision, the firm conducted a market survey to know the opinion of its consumers in Kolkata and Delhi. The surveys conducted in the two cities revealed that while 290 out of 400 consumers favoured the choice in Kolkata, only 160 out of 300 customers favoured the choice in Delhi. Can the firm conclude that the proportions of customers who favoured the actor in Kolkata and Delhi are the same? 26. A machine produced 20 defective items in a sample of 500. After the machine was overhauled, it produced 5 defective items in a batch of 150. Has the machine improved after overhauling? Chi Square Test 2 test 1. From a hospital record, the following data was obtained about the births of new born babies on various days of the week during the past year: Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total 184 148 145 153 150 154 116 1050 Can we conclude that the birth of a child is independent of the day in a week/ 2. The probabilities of having blood phenotype A, B, AB and O in a certain community is known to be 0.41, 0.10, 0.04 and 0.45 respectively. A blood sample was collected for 200 individuals selected at random from certain population and the following data were obtained: Blood phenotype A B AB O Number of persons 89 18 12 81 Do the data suggest that the individuals come from the above community? Test at 1% level. 3. The number of breakdowns of machines in a big factory was found as 20, 17, 12, 6, 8, 5, 16 and 14 during the last 8 months period. Test whether these frequencies are in agreement with the belief that occurrence of breakdowns was the same during the 8 months period. test 2 4. A behavioral scientist id conducting a survey to determine if the financial benefits , in terms of salary, influence the level of satisfaction of employees or whether there are other factors such as work environment which are more important than salary in influencing employee satisfaction. A random sample of 300 employees is given a test to determine their level of satisfaction. Their salary levels are also recorded. The information is tabulated as below: Level of satisfaction Annual salary (in Lac Rs) Up to 5 5 - 10 More than 10 High 10 10 10 Medium 50 45 15 Low 40 15 05 At 5% level of significance, determine whether the level of employee satisfaction is influenced by salary level? F-Test 1. With the help of the following data about daily prices of stocks, compare variations in two stocks listed on BSE. Date 05.10.15 06.10.15 09.10.15 10.1015 11.10.15 12.10.15 13.10.15 16.10.15 17.10.15 18.10.15 Assume 5 % level of significance. 2. Variances of past dividends are equal for two populations comprising companies in IT and Pharmaceutical sectors. To compare the variability of dividends declared for a year 9 companies were randomly selected from the IT sector and 8 companies were randomly selected from Pharmaceutical sectors. The sum of squares of dividends from their respective means were found to be 160 and 91 respectively. Can we conclude that the variability in dividends of the companies in the two sectors is the same