Tutorial Chapter 5 (Part A)_Statistical Analysis For Means.pdf - Adobe Reader X File Edit View Window Help Open 66.7% Tools Fill & Sign Comment TUTORIAL CHAPTER 5 (PART A): STATISTICAL ANALYSIS FOR MEANS 1. The government awarded grants to the agricultural departments of five universities to test the yield capabilities of two new varieties of paddy seeds, namely Malinja and Long Grain. Each variety was planted on plots of equal area at each university and the yields, in kilogram per plot are recorded as follows. University Variety 1 2 5 Malinja 38 23 35 41 44 Long Grain 45 25 31 38 50 Construct a 99% confidence interval on the mean difference of the two new varieties of paddy seeds. Then, provide an interpretation about the confidence interval. 2 Let X be equal to the access weight of soap in a "1000-gram" bottle. Assume that the distribution of X" is N(#, 169). What sample size is required so that we are 95% confident that the maximum error of the population mean is 1.5? 3. The following are the heated-producing capacities (in millions of calories per ton) of coal from two mines: Mine A 8500 8330 8480 7960 8030 Mine B |7710 7890 7920 8270 7860 Assuming that the data constitute independent random samples from normal populations with equal variances, (a) find the means and standard deviations for each type of mine. (b) construct a 90% confidence interval for the difference of two population means between the mines. Interpret your answer. 4. The manager of a vehicle company is testing two brands of radial tyres and assigns one tyre of each brand at random to the two rear wheels of eight cars and runs the cars until the tyres wear out. The distance (in thousands kilometres) travelled are as follow. Car 1 2 13 4 5 6 Brand ] 37 45 36 32 39 49 38 31 Brand 2 34 42 35 33 37 45 39 33 Find a 94% confidence interval on the mean difference in distance travelled for both brands of tyre.Tutorial Chapter 5 (Part A)_Statistical Analysis For Means.pdf - Adobe Reader X File Edit View Window Help Open 2 16 66.7% Tools Fill & Sign Comment TUTORIAL CHAPTER 5 (PART A): STATISTICAL ANALYSIS FOR MEANS 5. A study has been conducted to compare the nicotine contents of two brands of cigarettes. Ten random samples of cigarettes for Brand A has an average nicotine content of 3.1 milligrams with standard deviation of 0.5 milligram, while eight random selected samples of cigarettes for Brand B has an average nicotine content of 2.7 milligrams with a standard deviation of 0.7 milligram. Assume that the two sets of samples from both brands of cigarettes are independent random samples from normal populations with unequal variances. Construct a 99% confidence interval on the difference in mean of nicotine contents for two brands of cigarettes. Then, give a comment about the confidence interval. 6. A light bulb manufacturer sells a light bulb that has a mean life of 1450 hours with a standard deviation of 33.7 hours. A new manufacturing process is being tested and there is interest in knowing the mean life # of the new bulbs. How large a sample is required so that estimation error of 5 is a 95% confidence interval for #? 7. A researcher collected a simple random sample of the cents portions from 100 checks and from 100 credit card charges. The cents portions of the checks have a mean of 23.8 cents and a standard deviation of 32.0 cents. The cents portions of the credit charges have a mean of 47.6 cents and a standard deviation of 33.5 cents. Construct a 95% confidence interval for the difference between the means cents portions from checks and from credit card charges. Assume that the collected data constitute independent samples from normal populations with dissimilar standard deviations. A simple random sample of 13 four-cylinder cars is obtained, and the braking distances are measured. The mean braking distance is 137.5 ft and the standard deviation is 5.8 ft. A simple random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of 136.3 ft with a standard deviation of 9.7 ft. Construct a 90% confidence interval for the difference between the means braking distance of four-cylinder cars and six- cylinder cars. Assume that the measurements constitute independent samples from normal populations with dissimilar standard deviations.Tutorial Chapter 5 (Part A)_Statistical Analysis For Means.pdf - Adobe Reader X File Edit View Window Help Open 16 75% Tools Fill & Sign Comment 9. Thirteen tons of cheeses are stored in some old gypsum mines, including "10-kg" wheels (label weight). A random sample of n = 9 of these wheels yielded the following weights (in kilograms) TUTORIAL CHAPTER 5 (PART A): STATISTICAL ANALYSIS FOR MEANS 9.75 8.60 8.41 8.80 8.69 10.14 10.39 10.07 10.48 Assuming that the distribution of the weights of the wheels of cheese is N( u, o?)- (1) Find the values of sample mean and standard deviation (ii) Construct a 94% confidence interval for the true mean weight of cheese wheels yielded. 10. The length in centimeters of n=35 fish yielded an average length of X =16.82 and $2 =34.9. Determine the size of a new sample so that x 1 0.5 is an approximate 95% confidence interval for population mean, #. 11. A manufacturer of electric bulbs wants to find a 98% confidence interval for the lifetime of its new family of bulbs. How large a sample should be selected if the company seeks a confidence interval for population means no more than 20 hours in width? Assume that previous experience has shown that the population means and standard deviation of the lifetime of these bulbs is 19.5 and 30 hours respectively.Tutorial Chapter 5 (Part A)_Statistical Analysis For Means.pdf - Adobe Reader X File Edit View Window Help Open 3 16 66.7% Tools Fill & Sign Comment 12. The prices (in RM) for a particular model of digital camera with 16.0 megapixels and an optical 30X zoom lens are shown below for 10 online retailers 616 593 601 608 602 599 603 591 614 613 Assume the variable is normally distributed. (1) By using calculator, determine the values of sample mean and standard deviation. Write your answer with correct notations. (ii) Construct a 94% confidence interval for the true mean price. 13. A sample of 40 networking sites for a specific month has a mean of 26.1 and a standard deviation of 4.2. Find the 97% confidence interval of the population mean. 14. A manager decides to install a server in his company. He will install server A if it is having a significant short execution time compared to server B. Thus, he tested a certain computer algorithm 21 times in each server and the results are as follows. TUTORIAL CHAPTER 5 (PART A): STATISTICAL ANALYSIS FOR MEANS Execution time (minutes) Server B Sample mean 6.7 7.5 Sample standard deviation 0.6 09 Assuming that the observed times are approximately normal with similar standard deviation, construct a 98% confidence interval for the difference between the true means execution times on server A and server B. Hence, give a comment on the confidence interval. (ii) Based on your answer in (i), which server should be installed? Give a reason to support your answer.Tutorial Chapter 5 (Part A)_Statistical Analysis For Means.pdf - Adobe Reader X File Edit View Window Help * Open 4 + 125% Tools Fill & Sign Comment 15. An engineer in Tenaga Nasional Berhad confidently claim that the population mean of voltage level for the existent cable is between 40.05 and 46.74 volts. (i) A sample of 15 cables with variance of 9.79 is selected. With what level of confidence can that claim be made? (ii) After the observation, he decided to test two types of new insulation materials on 15 cables and the measurements of voltage level are recorded. The following table shows the difference of the voltage level for two types of new insulation. Cable 1 2 3 4 15 6 7 8 9 10 11 12 13 14 15 Difference of the 16 6 20 11 15 28 26 16 27 30 14 8 8 W voltage level Construct 94% confidence interval for the mean difference of voltage level between the two types of new insulation