Using the Wrong Distribution When testing a claim about a

Problem 4BSC 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.

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?

Problem 3BSC t Test Exercise 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? Exercise df If we are using the sample data from Exercise 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?

Problem 2BSC df If we are using the sample data from Exercise 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? Exercise 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 Teen-Rated 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?

Cigarette Nicotine The claim is that for the nicotine amounts in king-size cigarettes, \(\mu>1.10 \mathrm{mg}\). The sample size is \(n=25\) and the test statistic is \(t=3.349\). Equation Transcription: Text Transcription: \mu >1.10 mg n=25 t=3.349

Problem 35BB 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. Example 1? Cell Phone Radiation: ?P?-Value Method

Problem 6BSC Finding P-values. In Exercises, either use technology to find the P-value or use Table to find a range of values for the P-value. Cigarette Tar The claim is that for the tar amounts in king-size cigarettes, ? > 20.0 mg. The sample size is n = 25 and the test statistic is t = 1.733.

Car Crash Tests The claim is that for measurements of standard head injury criteria in car crash tests, \(\mu=475 H I C\). The sample size is \(n=21\) and the test statistic is \(t=-2.242\) Equation Transcription: Text Transcription: \mu=475 HIC n=21 t=-2.242

Testing Hypotheses. In Exercises 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 reduced-fat 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. Equation Transcription: Text Transcription: x-=19.6

Pulse Rates The claim is that for pulse rates of women, \(\mu=73\) . The sample size is \(n=40\) and the test statistic is \(t=2.463\). Equation Transcription: Text Transcription: \mu=73 n=40 t=2.463

Testing Hypotheses. In Exercises 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 \(n=62, x^{-}=1.911 \mathrm{lb}, \text { and } s=1.065 \mathrm{lb}\). 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. Equation Transcription: Text Transcription: n=62, x-=1.911 lb, and s=1.065 lb

Testing Hypotheses. In Exercises 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 \(n=50, x^{-}=9.81 \mathrm{~km}, \text { and } s=5.01 \mathrm{~km}\). 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. Equation Transcription: Text Transcription: n=50, x-=9.81 km, and s=5.01 km

Testing Hypotheses. In Exercises 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 \(n=82, x^{-}=35.9 \text { years and } s=11.1 \text { years }\). Use a 0.01 significance level to test the claim that the mean age of actresses when they win Oscars is 33 years. Equation Transcription: Text Transcription: n=82, x-=35.9 years and s=11.1 years

Problem 15BSC 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?

Problem 17BSC 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 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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?

Problem 18BSC 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 Sivertsen 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 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), 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 \(98.20^{\circ} \mathrm{F}\) and a standard deviation of \(0.62^{\circ} \mathrm{F}\) Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to \(98.6^{\circ} \mathrm{F}\), as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong? Equation Transcription: Text Transcription: 98.20°F 0.62°F 98.6°F

Problem 19BSC 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

Problem 21BSC 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

Problem 24BSC Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on 1-280 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

Testing Hypotheses. In Exercises 9–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), critical value(s), and state the final conclusion that addresses the original claim. Brain Volume Listed below are brain volumes \((\mathrm{cm} 3)\) 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 \(1100.0 \mathrm{~cm} 3\). Equation Transcription: Text Transcription: ( cm 3) 1100.0 cm 3

Problem 20BSC 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

Large Data Sets from Appendix B. In Exercises 25?28, use the data set from Appendix B to test the given claim. Identify the null hypothesis,alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value 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 25?28, use the data set from Appendix B to test the given claim. Identify the null hypothesis,alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value 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 25?28, use the data set from Appendix B to test the given claim. Identify the null hypothesis,alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value 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.

Problem 23BSC 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

Problem 28BSC use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Power SupplyData 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.

Hypothesis Tests with Known ? . In Exercises 29–32, conduct the hypothesis test using a known value of the population standard deviation \(\sigma\) . Repeat Exercise 11 assuming that the population standard deviation \(\sigma\) is known to be 11.1 years. Equation Transcription: Text Transcription: \sigma \sigma

Hypothesis Tests with Known \(\sigma\) . In Exercises 29–32, conduct the hypothesis test using a known value of the population standard deviation \(\sigma\) Repeat Exercise 9 assuming that the population standard deviation \(\sigma\) is known to be 3.8 chocolate chips. Equation Transcription: Text Transcription: \sigma \sigma \sigma

Problem 34BB 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 Distribution should be used for finding critical values and/or a T-value. 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.

Hypothesis Tests with Known \(\sigma\) . In Exercises 29–32, conduct the hypothesis test using a known value of the population standard deviation \(\sigma\) . Repeat Exercise 12 assuming that the population standard deviation \(\sigma\) is known to be 1.065 lb. Equation Transcription: Text Transcription: \sigma \sigma \sigma

Hypothesis Tests with Known \(\sigma\) . In Exercises 29–32, conduct the hypothesis test using a known value of the population standard deviation \(\sigma\) . Repeat Exercise 10 assuming that the population standard deviation \(\sigma\) is known to be 5.01 km Equation Transcription: Text Transcription: \sigma \sigma \sigma

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 \(t=d f \cdot(e A 2 / d f-1)\) where \(d f=n-1, e=2.718, A=z(8 \cdot d f+3) /(8 \cdot d f+1) \) 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 right-­tailed case. Compare the results to the critical t value of 1.655 found from STATDISK, Minitab, or a TI­-83/84 Plus calculator. Equation Transcription: Text Transcription: t=df( e A 2/ df-1) df=n-1, e=2.718, A=z (8df+3)/(8df+1) n=150

Problem 34BB 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 Distribution should be used for finding critical values and/or a T-value. 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.

Problem 35BB 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. Example 1 Cell Phone Radiation: P-Value Method