Mr. Bautista's Website - Announcements



DECSCI2 EXERCISES – HYPOTHESIS TESTINGTESTS CONCERNING MEANSA manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilograms. Test the hypothesis that μ = 8 kg against the alternative that μ ≠ 8 kg if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. Use a 0.01 level of significance.A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years, with a standard deviation of 8.9 years. Does this seem to indicate that the average life span today is greater than 70 years? Use a 0.05 level of significance.Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 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.The average length time for students to register for fall classes at a certain college has been known to be 50 minutes with a standard deviation of 10 minutes. A new registration procedure using modern computing machines is being implemented. If a random sample of 12 students had an average registration time of 42 minutes with a standard deviation of 11.9 minutes under the new system, test the hypothesis that the population mean is now less than 50, using a level of significance of 0.05. Assume the population of times to be normal.A course in mathematics is taught to 12 students by the conventional classroom procedure. A second group of 10 students was given the same course by means of programmed materials. At the end of the semester the same examination was given to each group. The 12 students meeting in the classroom made an average grade of 85 with a standard deviation of 4, while the 10 students using programmed materials made an average of 81 with a standard deviation of 5. Test the hypothesis that the two methods of learning are equal using a 0.10 level of significance. Assume the population to be approximately normal with equal variances.To determine whether membership in a fraternity is beneficial or detrimental to one’s grades, the following grade-point averages were collected over a period of 5 years:Year12345Fraternity2.02.02.32.12.4Non-fraternity2.21.92.52.32.4Assuming the populations to be normal, test at the 0.05 level of significance whether membership in a fraternity is detrimental to one’s grades.TESTING FOR PROPORTIONSA commonly prescribed drug on the market for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suffering from nervous tension showed that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance.A vote is to be taken among the residents of a town and the surrounding county to determine whether a civic center will be constructed. To determine if there is a significant difference in the proportion of town voters and county voters favoring the proposal, a poll is taken. If 120 of 200 town voters favor the proposal and 240 of 500 county residents favor it, would you agree that the proportion of town voters favoring the proposal is higher than the proportion of county voters? Use a 0.025 level of significance.MORE EXERCISESThe average height of females in the freshman class of a certain college has been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters, using a 0.05 level of significance?Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 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.A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms. To test this claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with a standard deviation of 5.61 kilograms. Test the manufacturer’s claim using a 0.05 level of significance.A study is made to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With the substrate concentration of 1.5 moles per liter, the reaction was run 15 times with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With a substrate concentration of 1.0 moles per liter, 12 runs were made yielding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Would you say that the increase in substrate concentration increases the mean velocity by more than 0.5 micromoles per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances.The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost (in thousands of dollars) for the two types of remodeling projects are as follows.Kitchen25.217.422.821.919.723.019.716.921.823.6Master Bedroom18.022.926.424.826.917.824.621.0Determine if there is a significant difference in the average costs for the two types of remodeling projects, using a 0.10 level of significance, and assuming equal variances.A taxi company is trying to decide whether the use of radial tires instead of 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 same test course. The gasoline consumption, in kilometers per liter, was recorded as follows:CarKilometers Per LiterRadial TiresBelted Tires14.24.124.74.936.66.247.06.956.76.864.54.475.75.786.05.897.46.9104.94.7116.16.0125.24.9At the 0.025 level of significance, 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.The gas company claims that two thirds of the houses in a certain city are heated by natural gas. Do we have reason to doubt this claim if, in a random sample of 1000 houses in this city, it is found that 618 are heated by natural gas? Use a 0.02 level of significance. A geneticist is interested in the proportion of males and females in a population that have a certain minor blood disorder. In a random sample of 100 males, 31 are found to be afflicted, whereas only 24 of 100 females tested appear to have the disorder. Can we conclude at the 0.01 level of significance that the proportion of men in the population afflicted with this blood disorder is significantly greater than the proportion of women afflicted?A firm is studying the delivery times of two raw material suppliers. The firm is basically satisfied with supplier A and is prepared to stay with that supplier. However, if the firm finds that the mean delivery time of supplier B is less than that of supplier A, it will begin making raw material purchases from supplier B. Assume that 50 independent samples from each supplier show the delivery time of supplier A to be 14 days with a standard deviation of 3 days, while the delivery time of B is shown to be 12.5 days with a standard deviation of 2 days. Testing at a 0.05 level of significance, should the firm switch to supplier B or not?Starting annual salaries for individuals with master’s and bachelor’s degrees were collected in two independent random samples. The average starting salary of a random sample of 60 individuals with master’s degrees showed a mean of $45,000 with a standard deviation of $4000, while those with bachelor’s degrees had a mean starting salary of $35,000 with a standard deviation of $3500. Test at a 0.05 level of significance if those with master’s degrees had a significantly higher average starting salary than those individuals with bachelor’s degrees.Starting annual salaries for individuals entering the public accounting and financial planning professions were presented in Fortune, June 26, 1995. The starting salaries for a sample of 12 public accountants and a sample of 14 financial planners follow, with data in thousands of dollars.Public Accountant: 30.631.228.935.225.133.231.335.331.030.129.9 24.4Financial Planner:31.626.625.525.025.932.926.925.827.529.623.9 26.924.425.5Test if the starting annual salaries of the accountants and financial planners are equal at a 0.05 level of significance, assuming unequal variances.Rental car gasoline prices per gallon were sampled at eight major airports. Data for Hertz and National car rental companies follow (USA Today, April 4, 2000).AirportHertzNationalBoston Logan1.551.56Chicago O’hare1.621.59Los Angeles1.721.78Miami1.651.49New York (JFK)1.721.51New York (LaGuardia)1.671.50Orange County1.681.77Washington1.521.41Test at a 0.05 level of significance if there is a difference between the gas prices of the two rental car companies.Figure Perfect Inc., is a women’s figure salon that specializes in weight reduction programs. Weights for a sample of clients before and after a 6-week introductory program are shown here.ClientWeight BeforeWeight After114013221601583210195414815251901806170164Determine at a 0.05 level of significance whether the introductory program provided a statistically significant weight loss.Yahoo! Internet Life sponsored surveys in several metropolitan areas to estimate the proportion of adults using the Internet at work (USA Today, May 7, 2000). Results showed 96 of 240 of Washington D.C. adults use the Internet at work, while 80 of 250 of San Francisco adults use the internet at work. Do the sample results indicate that the population proportion of adults using the Internet at work in Washington D.C. is greater then the population proportion in San Francisco? Use a 0.05 level of significance.A Business Week/Harris survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was “Do you think that there will be an increase in the number of full-time employees at your company over the next 12 months?” In May 1997, 220 of 400 executives answered yes, while in December 1996, 192 of 400 executives had answered yes. Test at a 0.04 level of significance if there was a significant increase in the proportion of executives who answered yes from December 1996 to May 1997. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download