Boardwork: Hypothesis Test

Boardwork: Hypothesis Test 10.25/357) Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample 0f 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal. 10.43/360) A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometres per liter, was recorded as follows; Kilometers per liter Car Radial Tires Belted Tires 1 4.2 4.1 2 4.7 4.9 3 6.6 6.2 4 7.0 6.9 5 6.7 6.8 6 4.5 4.4 7 5.7 5.7 8 6.0 5.8 9 7.4 6.9 10 4.9 4.7 11 6.1 6.0 12 5.2 4.9 Can we conclude that cars equipped with radial tires give better fuel economy than those equipped with belted tires? Assume the populations to be normally distributed. Use a P- value in your conclusion 10.60/366 At a certain college it is estimated that at most 25% of the students ride bicycles to class. Doe this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class? Use a .05 level of significance. 10.68/370 Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that  = 6 against the alternative that  < 6 if a random sample of 20 high school seniors has a standard deviations s = 4.51. use a .05 level of significance. 10.69/370 Afloxtoxins produced by mold on peanut crops in Virginia must be monitored. A sample of 64 batches of peanuts reveals levels of 24.17 ppm, on average, with a variance of 4.25 ppm. Test the hypothesis that 2 = 4.2 ppm with the alternative that 2  4.2 ppm. Use a P-value in your conclusions. 10.71/370 A soft-drink dispensing machine is said to be out of control if the variance of the contents exceeds 1.15 deciliters. If a random sample of 25 drinks from this machine has a variance of 2.03 deciliters, does this indicate at the 0.05 level of significance that the machine is out of control? Assume that the contents are approximately normally distributed. 10.73/370 A study is conducted to compare the length of time between men and women to assemble a certain product. Past experience indicates that the distribution of times for both men and women is approximately normal but the variance of the times for women is less than that of men. A random sample of times for 11 men and 14 women produced the following data: Men Women

n1 = 11 n2 = 14

s1 = 6.1 s2 = 5.3 Test the hypothesis that against the alternative that . Use a P-value in your conclusion. 10.77/371 An experiment was conducted to compare the alcohol contents in a soy sauce at two different production lines. Production was monitored eight times a day. The data are shown here. Production line 1: 0.48, 0.39, 0.42, 0.52, 0.40, 0.48, 0.52, 0.52 Production line 2: 0.38, 0.37, 0.39, 0.41, 0.38, 0.39, 0.40. 0.39

Assume both populations are normal. It is suspected that production line 1 is not producing as consistently as production line 2 in terms of alcohol contents. Test the hypothesis that 1 = 2 against the alternative that 1  2. Use a P-value. 10.81/383 A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans. At the 0.05 level of significance, test the hypothesis that the machine is mixing the nuts in the ration 5:2:2:1. 10.93/384 A criminologist conducted a survey to determine whether the incidence of certain types of crime varied from one part of a large city to another. The particular crimes of interest were assault, burglary, larceny, and homicide. The following table shows the numbers of crimes committed in four areas of the city during the past year.

Type of Crime District Assault Burglary Larceny Homicide 1 162 118 451 18 2 310 196 996 25 3 258 193 458 10 4 280 175 390 19 Can we conclude from these data at the .01 level of significance that the occurrence of these types of crime is dependent on the city district? 10.94/384 A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remedy was tried on 50 students and the following data recorded: Cough Remedy nyQuil Rubitussin Triaminic No relief 11 13 9 Some relief 32 28 27 Total relief 7 9 14 Test the hypothesis that the three cough remedies are equally effective. Use a P-value in your conclusion.