t Test Exercise 2 refers to a t test. What is a t test Why are the t test methods of

Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from Content and Ratings of TeenRated Video Games, by Haninger and Thompson, Journal of the American Medical Association, Vol. 291, No. 7). What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 sec? Are the requirements all satisfied? 84 14 583 50 0 57 207 43 178 0 2 57

df If we are using the sample data from Exercise 1 in a t test of the claim that the population mean is greater than 90 sec, what does df denote, and what is its value?

t Test Exercise 2 refers to a t test. What is a t test? Why are the t test methods of Part 1 in this section so much more likely to be used than the z test methods in Part 2?

Confidence Interval Assume that we will use the sample data from Exercise 1 with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < < 191.4 sec, what should we conclude about the claim?

Finding Pvalues. In Exercises 58, either use technology to find the Pvalue or use Table A3 to find a range of values for the Pvalue.Cigarette Nicotine The claim is that for the nicotine amounts in kingsize cigarettes, > 1.10 mg. The sample size is n = 25 and the test statistic is t = 3.349

Finding Pvalues. In Exercises 58, either use technology to find the Pvalue or use Table A3 to find a range of values for the Pvalue.Cigarette Tar The claim is that for the tar amounts in kingsize cigarettes, > 20.0 mg. The sample size is n = 25 and the test statistic is t = 1.733 .

Finding Pvalues. In Exercises 58, either use technology to find the Pvalue or use Table A3 to find a range of values for the Pvalue.Car Crash Tests The claim is that for measurements of standard head injury criteria in car crash tests, = 475 HIC. The sample size is n = 21 and the test statistic is t = 2.242 .

Finding Pvalues. In Exercises 58, either use technology to find the Pvalue or use Table A3 to find a range of values for the Pvalue.Pulse Rates The claim is that for pulse rates of women, = 73 . The sample size is n = 40 and the test statistic is t = 2.463 .

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Chocolate Chip Cookies The Chapter Problem for Chapter 3 includes the sample mean of the numbers of chocolate chips in 40 Chips Ahoy reduced fat cookies. The sample mean is x = 19.6 chocolate chips and the sample standard deviation is 3.8 chocolate chips. Use a 0.05 significance level to test the claim that Chips Ahoy reducedfat cookies have less fat because they have a mean number of chocolate chips that is less than the mean of 24 for regular Chips Ahoy cookies. See the accompanying TI83/84 Plus display that results from this hypothesis test. TI83/84 PLUS d

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.. Earthquake Depths Data Set 16 in Appendix B lists earthquake depths, and the summary statistics are n = 50 , x = 9.81 km, and s = 5.01 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean depth equal to 10 km. See the accompanying Minitab display that results from this hypothesis test. MINITAB d

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.OscarWinning Actresses Data Set 11 in Appendix B lists ages of actresses when they won Oscars, and the summary statistics are n = 82 , x = 35.9 years, and s = 11.1 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win Oscars is 33 years.

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Discarded Plastic The weights (lb) of discarded plastic from a sample of households is listed in Data Set 23 in Appendix B, and the summary statistics are n = 62 , x = 1.911 lb, and s = 1.065 lb. Use a 0.05 significance level to test the claim that the mean weight of discarded plastic from the population of households is greater than 1.800 lb.

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim. M&M Weights A simple random sample of the weights of 19 green M&Ms has a mean of 0.8635 g and a standard deviation of 0.0570 g (as in Data Set 20 in Appendix B). Use a 0.05 significance level to test the claim that the mean weight of all green M&Ms is equal to 0.8535 g, which is the mean weight required so that M&Ms have the weight printed on the package label. Do green M&Ms appear to have weights consistent with the package label?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Human Body Temperature Data Set 3 in Appendix B includes a sample of 106 body temperatures with a mean of 98.20 F and a standard deviation of 0.62 F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.. Is the Diet Practical? When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction, by Dansinger, et al., Journal of the American Medical Association, Vol. 293, No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0. Based on these results, does the diet appear to be effective? Does the diet appear to have practical significance?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Flight Delays Data Set 15 in Appendix B lists 48 different departure delay times (minutes) for American Airlines flights from New York (JFK) to Los Angeles. Negative departure delay times correspond to flights that departed early. The mean of the 48 times is 10.5 min and the standard deviation is 30.8 min. Use a 0.01 significance level to test the claim that the mean departure delay time for all such flights is less than 12.0 min. Is a flight operations manager justified in reporting that the mean departure time is less than 12.0 min?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.4 and a standard deviation of 21.0 (based on data from Effect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia, by Gardner et al., Archives of Internal Medicine, Vol. 167). Test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim. Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug Zopiclone for treating insomnia in older subjects. Before treatment with Zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with Zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults, by Siversten, et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 min. Does Zopiclone appear to be effective?

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Years in College Listed below are the numbers of years it took for a random sample of college students to earn bachelor's degrees (based on data from the National Center for Education Statistics). Use a 0.01 significance level to test the claim that for all college students,the mean time required to earn a bachelor's degree is greater than 4.0 years. Is there anything about the data that would suggest that the conclusion might not be valid? 4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5 6 6 8 9 9 13 13 15

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Ages of Race Car Drivers Listed below are the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Use a 0.05 significance level to test the claim that the mean age of all race car drivers is greater than 30 years. 32 32 33 33 41 29 38 32 33 23 27 45 52 29 25

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim. Lead in Medicine Listed below are the lead concentrations (in g / g ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States. The data are based on the article Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet, by Saper, et al., Journal of the American Medical Association, Vol. 300, No. 8. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 g / g. 3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.. Brain Volume Listed below are brain volumes ( cm 3 ) of unrelated subjects used in a study. (See Data Set 6 in Appendix B.) Use a 0.01 significance level to test the claim that the population of brain volumes has a mean equal to 1100.0 cm 3 . 963 1027 1272 1079 1070 1173 1067 1347 1100 1204

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Heights of Supermodels Listed below are the heights (inches) for the simple random sample of supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr, Kroes, and Swanepoel. Use a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean height of 63.8 in. for women in the general population. Given that there are only 10 heights represented, can we really conclude that supermodels are taller than the typical woman? 70 71 69.25 68.5 69 70 71 70 70 69.5

Testing Hypotheses. In Exercises 924, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the Pvalue method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, Pvalue (or range of Pvalues), critical value(s), and state the final conclusion that addresses the original claim.Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on I280 near Cupertino, California (based on data from SigAlert). This simple random sample was obtained at 3:30 p.m. on a weekday. Use a 0.05 significance level to test the claim that the sample is from a population with a mean that is less than the speed limit of 65 mi/h. 62 61 61 57 61 54 59 58 59 69 60 67

Large Data Sets from Appendix B. In Exercises 2528, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvalue method unless your instructor specifies otherwise.Earthquake Magnitudes Use the earthquake magnitudes listed in Data Set 16 in Appendix B and test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.05 significance level.

Large Data Sets from Appendix B. In Exercises 2528, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvalue method unless your instructor specifies otherwise. Blood Pressure Use the systolic blood pressure measurements for females lised in Data Set 1 in Appendix B and test the claim that the female population has a mean systolic blood pressure level less than 120.0 mm Hg. Use a 0.05 significance level.

Large Data Sets from Appendix B. In Exercises 2528, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvalue method unless your instructor specifies otherwise.College Weights Use the September weights of males in Data Set 4 from Appendix B and test the claim that male college students have a mean weight that is less than the 83 kg mean weight of males in the general population. Use a 0.01 significance level.

Large Data Sets from Appendix B. In Exercises 2528, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, Pvalue or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the Pvalue method unless your instructor specifies otherwise.Power Supply Data Set 18 in Appendix B lists measured voltage amounts supplied directly to the author's home. The Central Hudson power supply company states that it has a target power supply of 120 volts. Using those home voltage amounts, test the claim that the mean is 120 volts. Use a 0.01 significance level.

In Exercises 2932, conduct the hypothesis test using a known value of the population standard deviation . Repeat Exercise 9 assuming that the population standard deviation is known to be 3.8 chocolate chips.

In Exercises 2932, conduct the hypothesis test using a known value of the population standard deviationRepeat Exercise 10 assuming that the population standard deviation is known to be 5.01 km.

In Exercises 2932, conduct the hypothesis test using a known value of the population standard deviationRepeat Exercise 11 assuming that the population standard deviation is known to be 11.1 years.

In Exercises 2932, conduct the hypothesis test using a known value of the population standard deviationRepeat Exercise 12 assuming that the population standard deviation is known to be 1.065 lb

Finding Critical t Values When finding critical values, we sometimes need significance levels other than those available in Table A3. Some computer programs approximate critical t values by calculating t = df ( e A 2 / df 1 ) where df = n 1 , e = 2.718 , A = z ( 8 df + 3 ) / ( 8 df + 1 ) and z is the critical z score. Use this approximation to find the critical t score corresponding to n = 150 and a significance level of 0.05 in a righttailed case. Compare the results to the critical t value of 1.655 found from STATDISK, Minitab, or a TI83/84 Plus calculator.

Using the Wrong Distribution When testing a claim about a population mean with a simple random sample selected from a normally distributed population with unknown , the Student t distribution should be used for finding critical values and/or a Pvalue. If the standard normal distribution is incorrectly used instead, does that mistake make you more or less likely to reject the null hypothesis, or does it not make a difference? Explain.

Interpreting Power For Example 1 in this section, the hypothesis test has power of 0.4274 of supporting the claim that < 1.00 W / kg when the actual population mean is 0.80 W/kg. a. Interpret the given value of the power. b. Identify the value of and interpret that value