Instructions: Test variances or standard deviations, using the chi-square test. Finding the chi-square critical value for a specific a when the hypothesis test is right-tailed. Finding the chi-square critical value for a specific a when the hypothesis test is left-tailed. Finding the chi-square critical values for a specific a when the hypothesis test is two-tailed. Question: 3. Calories in Pancake Syrup A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60. A sample of major brands of syrup is selected, and the number of calories is shown. At a 0.10, can the claim be rejected? 53 210 100 200 100 220 210 100 240 200 100 210 100 210 100 210 100 60 Source: Based on information from The Complete Book of Food Counts by Corrine T. Netzer, Dell Publishers, New York. 4. High Temperatures in January Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows: 55, 44, 51, 59, 62, 60, 46, 51, 37, 30, 46, 51, 53, 57, 57, 39, 28, 37, 35, and 28 degrees Fahrenheit. The normal standard deviation in high temperatures for this time period is usually no more than 8 degrees. A meteorologist believes that with the unusual trend intemperatures the standard deviation is greater. At a 0.05, can we conclude that the standard deviation is greater than 8 degrees? Source: www.wunderground.com 5. Stolen Aircraft Test the claim that the standard deviation of the number of aircraft stolen each year in the United States is less than 15 if a sample of 12 years had a standard deviation of 13.6. Use a 0.05. Source: Aviation Crime Prevention Institute. 6. Carbohydrates in Fast Foods The number of carbohydrates found in a random sample of fast-food entrees is listed below. Is there sufficient evidence to conclude that the variance differs from 100? Use the 0.05 level of significance. 53 46 39 39 30 47 38 73 43 41 Source: Fast Food Explorer (www.fatcalories.com). 7. Transferring Phone Calls The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.2 minutes or less. A sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.8 minutes. At a 0.01, test the claim that the standard deviation is less than or equal to 1.2 minutes. Use the P-value method. 8. Soda Bottle Content A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.03 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At a 0.05, can we reject the claim that the machine is functioning properly? Use the P-value method. 12.03 12.10 12.02 11.98 12.00 12.05 11.97 11.99 9. High-Potassium Foods Potassium is important to good health in keeping fluids and minerals balanced and blood pressure low. High-potassium foods are those that contain more than 200 mg per serving. The amounts of potassium for a random sample are shown. At a 0.10 is the standard deviation of the potassium content greater than 100? 781 467 508 530 707 535 498 400 Source: www.drugs.com 10. Exam Grades A statistics professor is used to having a variance in his class grades of no more than 100. He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below.) At a 0.05, can it be concluded that the variance in grades exceeds 100? 92.3 89.4 76.9 65.2 49.1 96.7 69.5 72.8 67.5 52.8 88.5 79.2 72.9 68.7 75.8 11. Tornado Deaths A researcher claims that the standard deviation of the number of deaths annually from tornadoes in the United States is less than 35. If a sample of 11 randomly selected years had a standard deviation of 32, is the claim believable? Use a 0.05. Source: National Oceanic and Atmospheric Administration. 12. Interstate Speeds It has been reported that the standard deviation of the speeds of drivers on Interstate 75 near Findlay, Ohio, is 8 miles per hour for all vehicles. A driver feels from experience that this is very low. A survey is conducted, and for 50 drivers the standard deviation is 10.5 miles per hour. At a 0.05, is the driver correct? 13. College Room and Board Costs Room and board fees for a random sample of independent religious colleges are listed below. 7460 7959 7650 8120 7220 8768 7650 8400 7860 6782 8754 7443 9500 9100 Estimate the standard deviation in costs based on s R4. Is there sufficient evidence to conclude that the sample standard deviation differs from this estimated amount? Use a 0.05. Source: World Almanac. 14. Heights of Volcanoes A sample of heights (in feet) of active volcanoes in North America, outside of Alaska, is listed below. Is there sufficient evidence that the standard deviation in heights of volcanoes outside Alaska is less than the standard deviation in heights of Alaskan volcanoes, which is 2385.9 feet? Use a 0.05. 10,777 8159 11,240 10,456 14,163 8363 Source: Time Almanac. 15. Manufactured Machine Parts A manufacturing process produces machine parts with measurements the standard deviation of which must be no more than 0.52 mm. A random sample of 20 parts in a given lot revealed a standard deviation in measurement of 0.568 mm. Is there sufficient evidence at a 0.05 to conclude that the standard deviation of the parts is outside the required guidelines