The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gas emissions? 5 Click the icon to view the data. What are the hypotheses for this test? A. H0 : At least one of the means is different from the others. H1: μ1 = μ2 = μ3 B. H0: μ1 ≠ μ2 ≠ μ3 H1: μ1 = μ2 = μ3 C. H0: μ1 = μ2 = μ3 H1 : At least one of the means is different from the others. D. H0: μ1 = μ2 = μ3 H1: μ1 ≠ μ2 ≠ μ3 Determine the test statistic. F = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to two decimal places as needed.) What is the conclusion of the test? (1) __ the null hypothesis. Conclude that the type of vehicle (2) amount of greenhouse gas emissions for these three types. Type A Type B Type C (1) Reject (2) does not Do not reject does
Use the technology display, which results from the head injury measurements from car crash dummies listed below. The measurements are in hic (head injury criterion) units, and they are from the same cars used for the table below. Use a 0.01 significance level to test the given claim. Test the null hypothesis that head injury measurements are not affected by an interaction between the type of car (foreign, domestic) and size of the car (small, medium, large). What do you conclude? 6 Click the icon to view the data table and technology display. What are the null and alternative hypotheses? A. H0 : Head injury measurements are affected by an interaction between type of car and size of the car. H1 : Head injury measurements are not affected by an interaction between type of car and size of the car. C. H0 : Head injury measurements are not affected by type of car. H1 : Head injury measurements are affected by type of car. B. H0 : Head injury measurements are not affected by an interaction between type of car and size of the car. H1 : Head injury measurements are affected by an interaction between type of car and size of the car. D. H0 : Head injury measurements are not affected by size of car. H1 : Head injury measurements are affected by size of car. Find the test statistic. F = (Round to two decimal places as needed.) Determine the P-value. P-value = (Round to three decimal places as needed.) Determine whether there is sufficient evidence to support the given alternative hypothesis. Since the P-value is (1) 0.01, (2) H0. There is (3) evidence to support the alternative hypothesis. Conclude that there (4) appear to be an effect from an interaction between the type of car (foreign or domestic) and whether the car is small, medium, or large. 6: Data Table Size of Car Small Medium Large Foreign 292 244 355 533 512 670 505 399 337 Domestic 405 473 212 377 365 329 371 348 164 Source DF SS MS F P Type 1 35823 35822.7 2.60 0.133 Size 2 14905 7452.7 0.54 0.596 Interaction 2 41500 20750.2 1.51 0.261 Error 12 165354 13779.5 Total 17 257583 (1) less than or equal to (2) reject (3) sufficient (4) does not greater than fail to reject insufficient does
For a sample of eight bears, researchers measured the distances around the bears’ chests and weighed the bears Minitab was used to find that the value of the linear correlation coefficient is 𝑟 = 0.771. Using 𝛼 = 0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? Click here to view a table of critical values for the correlation coefficient. 1 a. Is there a linear correlation between chest size and weight? A. No, because the absolute value of the test statistic exceeds the critical value of 0.707 . B. Yes, because the test statistic falls between the critical values of -0.707 and 0.707 . C. Yes, because the absolute value of the test statistic exceeds the critical value of 0.707 . D. The answer cannot be determined from the given information. b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? (Round to three decimal places as needed.) 1: Table of Critical Values
Use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find (a) the pooled estimate p‾, (b) the z test statistic, (c) the critical z-values, and (d) the P-value. Treatment Group Placebo Group n1 = 320 n2 = 1000 x1 = 40 x2 = 100 (a) p‾ = (Round to three decimal places as needed.) (b) z = (Do not round until the final answer. Then round to two decimal places as needed.) (c) Choose the correct critical z-values below. A. ± 2.575 B. ± 1.645 C. ± 1.96 (d) The P-value is (Round to four decimal places as needed.)
The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts a-c. Height (x) 150 107 120 138 145 127 124 123 Interval after (y) 83 62 66 80 84 78 67 73 Click here to view a table of critical values for the correlation coefficient. 2 a. Find the value of the linear correlation coefficient r. r = (Round to three decimal places as needed.) b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using α = 0.05. The critical values are ± (Round to three decimal places as needed.) c. Is there sufficient evidence to conclude that there is a linear correlation between the two variables? A. No, because the absolute value of the correlation coefficient is greater than the critical value. B. Yes, because the absolute value of the correlation coefficient is greater than the critical value. C. Yes, because the absolute value of the correlation coefficient is less than the critical value. D. No, because the absolute value of the correlation coefficient is less than the critical value.
In a survey, 22% of 235 single women said that they "definitely want to have children." In the same survey, 27% of 265 single men gave the same response. Construct a 95% confidence interval estimate of the difference between the proportions of single women and single men who definitely want to have children. Is there a gender gap? Construct a 95% confidence interval estimate. < p1 - p2 < (Round to three decimal places as needed.) Is there a gender gap? Choose the correct answer below. A. Since the interval contains 0 , there is no evidence of a gender gap. B. Since the interval contains 0 , there is evidence of a gender gap. C. Since the interval does not contain 0 , there is no evidence of a gender gap. D. Since the interval does not contain 0 , there is evidence of a gender gap.
The blood pressure measurements of a single patient were taken by twelve different medical students and the results are listed below. Answer parts a-c. systolic (x) 13 6 13 3 14 2 11 9 12 2 12 2 12 9 13 2 13 5 14 3 141 13 8 diastolic (y) 94 93 10 0 84 88 83 81 85 80 95 10 6 97 Click here to view a table of critical values for the correlation coefficient. 3 a. Find the value of the linear correlation coefficient r. r = (Round to three decimal places as needed.) b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using α = 0.05. The critical values are ± . (Round to three decimal places as needed.) c. Is there sufficient evidence to conclude that there is a linear correlation between the two variables? A. Yes, because the absolute value of the correlation coefficient is less than the critical value. B. No, because the absolute value of the correlation coefficient is less than the critical value. C. Yes, because the absolute value of the correlation coefficient is greater than the critical value. D. No, because the absolute value of the correlation coefficient is greater than the critical value.
A survey of 407 workers showed that 129 said it was unethical to monitor employee e-mail. When 147 senior-level bosses were surveyed, 46 said it was unethical to monitor employee e-mail. Use a 0.05 significance level to test the claim that for those saying that monitoring e-mail is unethical, the proportion of employees is greater than the proportion of bosses. What is the conclusion of this hypothesis test? A. There is not sufficient evidence to support the claim that the proportion of employees is greater than the proportion of bosses. B. There is sufficient evidence to support the claim that the proportion of employees is greater than the proportion of bosses. C. There is not sufficient evidence to support the claim that the proportion of employees is less than the proportion of bosses. D. There is sufficient evidence to support the claim that the proportion of employees is less than the proportion of bosses.
The data below shows height (in inches) and pulse rates (in beats per minute) of a random sample of women. Answer parts a-c. height (x) 64.9 66.3 60.2 63.5 59.3 63.9 60.1 63.6 67.5 60.1 67.4 66.2 pulse rate (y) 79 73 86 60 72 69 81 62 66 70 85 78 Click here to view a table of critical values for the correlation coefficient. 4 a. Find the value of the linear correlation coefficient r. r = (Round to three decimal places as needed.) b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using α = 0.05. The critical values are ± . (Round to three decimal places as needed.) c. Is there sufficient evidence to conclude that there is a linear correlation between the two variables? A. Yes, because the absolute value of the correlation coefficient is less than the critical value. B. No, because the absolute value of the correlation coefficient is less than the critical value. C. Yes, because the absolute value of the correlation coefficient is greater than the critical value. D. No, because the absolute value of the correlation coefficient is greater than the critical value
In a clinical trial of a drug, 2.9% of the 1664 treated subjects experienced nausea. Among the 1662 subjects given placebos, 1.6% experienced nausea. Use a 0.05 significance level to test the claim that the incidence of nausea is greater among those who use the drug. What is the conclusion of the hypothesis test? A. There is sufficient evidence to support the claim that the incidence of nausea is greater among those who use the drug. B. There is not sufficient evidence to support the claim that the incidence of nausea is less among those who use the drug. C. There is not sufficient evidence to support the claim that the incidence of nausea is greater among those who use the drug. D. There is sufficient evidence to support the claim that the incidence of nausea is less among those who use the drug.
The heights (in inches) and pulse rates (in beats per minute) for a sample of 50 women were measured. Using technology with the paired height/pulse data, the linear correlation coefficient is found to be 0.290. Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women? Use a significance level of α = 0.05. Click here to view a table of critical values for the correlation coefficient. 5 Because |0.290| is (1) than the critical value, there (2) sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of α = 0.05.
A study comparing birth weight to IQ found 255 subjects (sample 1) with extremely low birth weights had IQ scores at age 8 with a mean of 93.9 and a standard deviation of 15.6. The control group of 282 subjects (sample 2) with normal birth weights had IQ scores with a mean of 95.4 and a standard deviation of 13.2 at age 8. Construct a 95% confidence interval estimate of the difference between the mean IQs of the two groups. Do not assume the population standard deviations are equal. Does IQ score appear to be affected by weight? 1 Click the icon to view the table of critical values. Find the 95% confidence interval. < μ1 - μ2 < (Round to two decimal places as needed.) Does the confidence interval show that low birth weight affects IQ? A. No, because the confidence interval does not include zero. B. Yes, because the confidence interval includes zero. C. Yes, because the confidence interval does not include zero. D. No, because the confidence interval includes zero.
Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.941 and the equation of the regression line is yˆ = -17.09 + 1.17x, where x represents the IQ score of the husband. Also, the 20x values have a mean of 102.89 and the 20y values have a mean of 103.65. What is the best predicted IQ of the wife, given that the husband has an IQ of 103? Use a significance level of 0.05. 6 Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the wife is (Round to two decimal places as needed.) 6: Critical Values of the Pearson Correlation Coefficient r
The heights are measured for the simple random sample of 9 supermodels. They have a mean height of 66.6 inches and a standard deviation of 1.9 inches. A sample is taken of the heights of 40 women who are not supermodels and they have heights with a mean of 66.3 inches and a standard deviation of 2.3 inches. Use a 0.10 significance level to test the claim that the mean height of supermodels is greater than the mean height of women who are not supermodels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. 2 Click the icon to view the table of critical values. (1) sufficient evidence that the mean height of supermodels is greater than the mean height of women who are not supermodels. 2: Critical Values
The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 132 feet. Use a significance level of 0.05. Height (ft) 96 128 75 128 88 73 80 96 Interval after (min) 66 85 59 86 70 75 73 75 7 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? yˆ = x (Round to two decimal places as needed.) What is the best predicted time for the interval after an eruption that is 132 feet high? The best predicted interval time for an eruption that is 132 feet high is minutes. (Round to one decimal place as needed.) 7: Critical Values of the Pearson Correlation Coefficient r
Scientists collect a simple random sample of 25 menthol cigarettes and 25 nonmenthol cigarettes. The menthol cigarettes have a mean nicotine amount of 0.85mg and a standard deviation of 0.32mg. The nonmenthol cigarettes have a mean nicotine amount of 0.96mg and a standard deviation of 0.23mg. Use a 0.05 significance level to test the claim that menthol cigarettes and nonmenthol cigarettes have different amounts of nicotine. Does menthol appear to have an affect on the nicotine content? Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. 3 Click the icon to view the table of critical values. (1) H0. There (2) (2) sufficient evidence that the menthol cigarettes and nonmenthol cigarettes have different amounts of nicotine. Does menthol appear to have an affect on the nicotine content? (3) , menthol (4) appear to have an affect on the nicotine content.
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 31 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 4000lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 31 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? 8 Click the icon to view the Minitab display. The linear correlation coefficient is (Round to three decimal places as needed.) Is there sufficient evidence to support a claim of linear correlation? Yes No 8: Minitab output The regression equation is Highway = 50.5 - 0.00507 Weight Predictor Coef SE Coef T P Constant 50.492 2.746 17.86 0.000 Weight -0.0050687 0.0007969 -7.91 0.000 S = 2.13781 R - Sq = 64.9% R - Sq(adj ) = 62.4% Predicted Values for New Observations New Obs Fit SE Fit 95% Cl 95% PI 1 30.217 0.517 (29.199, 31.235) (25.621, 34.813) Values of Predictors for New Observations New Obs Weight 1 4000
Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = x - y, find d‾, sd, the t test statistic, and the critical values to test the claim that μd = 0. x 8 14 15 18 13 8 17 7 y 7 13 11 14 8 6 15 8 d̅ = (Round to three decimal places as needed.) sd = (Round to three decimal places as needed.) t = (Round to three decimal places as needed.) tα/2 = ± (Round to three decimal places as needed.)
Eight different medical students took blood pressure measurements of the same patient and the results are listed below. The regression equation is yˆ = -71.377267 + 1.205562x and the standard error of the estimate is 2.7242 . Assume that the necessary conditions of normality and variance are met, and answer parts a and b. systolic (x) 138 130 139 140 120 127 122 130 diastolic (y) 95 89 98 93 71 82 75 87 a. Find the predicted diastolic reading given that the systolic reading is 122 . (Round to three decimal places as needed.) b. Find a 95% prediction interval estimate of the diastolic reading given that the systolic reading is 122 . < y < (Round to one decimal place as needed.)
Listed below are body mass indices (BMI) of a sample of college students. The BMI of each student was measured in September and April of the freshman year. Use a 0.05 significance level to test the claim that the mean change in BMI for all students is equal to 0 . Does BMI appear to change during freshman year? Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. April BMI 22.61 23.19 19.24 16.89 20.77 September BMI 22.40 22.76 19.48 17.63 19.59 Since the test statistic (1) in the critical region, (2) the null hypothesis. There (3) sufficient evidence to warrant rejection of the claim that for the population of students, the mean change in BMI from September to April is equal to 0 . (1) falls (2) reject (3) is not does not fall fail to reject is
Over the years, it was noticed that the cost of a slice of pizza and the cost of a subway fare in a certain city seemed to increase by the same amounts. Let x represent the cost of a slice of pizza and let y represent the corresponding subway fare. Use the following statistics that were obtained from a random sample of costs (in dollars) of pizza/subway fares to construct a prediction interval estimate of the subway fare with 99% confidence when the cost of a slice of pizza is $2.40. n = 6 b0 = 0.03456 b1 = 0.94502 x‾ = 1.0833333 ∑ x = 6.50 ∑ x^2 = 9.77 se = 0.123 The 99% prediction interval is < y < (Round to two decimal places as needed.)
Listed below are ages of actresses and actors from a country at the times that they won a certain award. The data are paired according to the years that they won. Use a 0.01 significance level to test the belief that best actresses are younger than best actors. Does the result suggest a problem in that culture? Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Best Actresses 2 4 2 6 2 9 3 5 2 7 3 7 3 3 3 5 2 1 2 7 4 0 2 5 2 7 3 2 2 8 Best Actors 4 0 3 4 4 1 2 9 4 8 3 6 4 2 2 5 6 2 4 1 4 9 5 6 5 2 4 1 2 6 Since the test statistic (1) in the critical region, (2) H0. There is (3) evidence to support the belief that best actresses are younger than best actors. This result appears to suggest that there (4) a problem in that culture. (1) falls (2) reject (3) insufficient (4) is does not fall fail to reject sufficient is not
Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 30, 32, 47, 37, 26, 28. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. 1 The test statistic is (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) The 𝑃-value is (Round to four decimal places as needed.) State the conclusion. (1) H0. There (2) sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes (3) to be equally likely, so the loaded die (4) to behave differently from a fair die. 1: Chi-square distribution table
The table provides the numbers of games of World Series contests along with the expected proportions with teams of equal abilities. Use a 0.05 significance level to test the claim that observed frequencies agree with theoretical proportions. Does there appear to be enough evidence to support the claim that seven-game series occur more often than expected? Games Actual World Series contests Expected proportion 4 5 6 7 19 21 23 38 3/16 3/16 4/16 6/16 Click here to view the chi-square distribution table. 2 Does there appear to be evidence to support the claim that seven-game series occur more often than expected? A. Yes, because there is sufficient evidence to reject the null hypothesis. B. No, because there is not sufficient evidence to reject the null hypothesis. C. Yes, because there is not sufficient evidence to reject the null hypothesis. D. No, because there is sufficient evidence to reject the null hypothesis.
Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion. A package of 100 candies are distributed with the following color percentages: 15% red, 19% orange, 13% yellow, 13% brown, 24% blue, and 16% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.01 significance level. 3 Click the icon to view the color counts for the candy in the package. Click here to view the chi-square distribution table. 4 The test statistic is (Round to two decimal places as needed.) The critical value is (Round to three decimal places as needed.) The P-value is (Round to three decimal placees as needed.) State the conclusion. (1) __ H0. There (2) sufficient evidence to warrant rejection of the claim that the color distribution is as claimed. 3: Candy Package Counts Candy Counts Color Number in Package Red 15 Orange 24 Yellow 10 Brown 4 Blue 27 Green 20
When flipping or spinning a penny, is the probability of getting heads the same? Use the data in the table below with a 0.05 significance level to test the claim that the proportion of heads is the same with flipping as with spinning. Heads Tails Flipping 12,076 10,225 Spinning 11,338 14,120 Is the proportion of heads the same with flipping as with spinning? A. Yes, there is sufficient evidence to reject the claim of homogeneity. B. No, there is sufficient evidence to reject the claim of independence. C. Yes, there is not sufficient evidence to reject the claim of independence. D. No, there is sufficient evidence to reject the claim of homogeneity.
Use the data in the table and a 0.05 significance level to test the claim that occupation is independent of whether the cause of death was homicide. Does any particular occupation appear to be most prone to homicides? If so, which one? Police Cashiers Taxi Drivers Guards Homicide 115 86 95 112 Cause of death other than homicide 78 32 84 83 Which particular occupation appears to be the most prone to homicides? A. Police are the most prone to homicides. B. No particular occupation appears to be the most prone to homicides. C. Taxi drivers are the most prone to homicides. D. Cashiers are the most prone to homicides. E. Guards are most prone to homicides.
In a test of weight loss programs, 144 subjects were divided such that 36 subjects followed each of 4 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.025 significance level to test the claim that the mean weight loss is the same for the different diets. Source of Variation SS df MS F P-value F crit Between Groups 341.456 3 113.81857 3.6697 0.013871 3.210775 Within Groups 4342.208 140 31.01577 Total 4683.664 143 Should the null hypothesis that all the diets have the same mean weight loss be rejected? A. No, because the P-value is greater than the significance level. B. Yes, because the P-value is greater than the significance level. C. No, because the P-value is less than the significance level. D. Yes, because the P-value is less than the significance level.
The data was obtained from car crash experiments. The table values are the Subcompact: 59 59 52 51 59 chest deceleration data (g) for the dummy in the driver's seat. Use a 0.05 significance level to test the null hypothesis that the different weight Compact: 51 46 46 53 47 categories have the same mean. Do the data suggest that larger cars are Midsize: 47 53 46 45 53 safer? Full-size: 48 43 40 41 Should the null hypothesis be rejected? A. No, because the P-value is greater than the significance level. B. Yes, because the P-value is less than the significance level. C. Yes, because the P-value is greater than the significance level. D. No, because the P-value is less than the significance level. Do the data suggest that larger cars are safer? A. No. The null hypothesis is rejected, but the data suggest that the mean deceleration for larger cars is larger, not smaller. B. Yes, because the null hypothesis is rejected. The data suggest that the mean deceleration for larger cars is smaller. C. No, because the null hypothesis is not rejected. There is not sufficient evidence to state that any of the means are different from the rest.
The following table shows the two-way ANOVA output for the weights of poplar trees. Assuming no interaction between site and treatment, is there sufficient evidence to support the claim that site has an effect on weight? Source DF SS MS F P Site 1 0.9907 0.990739 5.27 0.027 Treatment 3 0.6768 0.225595 1.20 0.322 Interaction 3 0.3722 0.124077 0.66 0.583 Error 40 7.5198 0.187996 Total 47 9.5595 Is there any evidence that site has an effect? (Assume a 0.05 significance level.) A. Since the P-value for site is small, there is no evidence to support the claim. B. Since the P-value for site is large, there is evidence to support the claim. C. Since the P-value for site is large, there is no evidence to support the claim. D. Since the P-value for site is small, there is evidence to support the claim.
Find the Taylor polynomial T2(x) for the function f(x) = ln(1 + x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-1/3, 1/3]. Which of the following is true for all values of x in I? |f(x) - T2(x)| ≤ 0.0418 |f(x) - T2(x)| ≤ 0.2083 All of the above. None of the above.
For approximately what values of x can you replace sin x by x – x^3/6 with an error of magnitude no greater than 8×10^-5 ? (Round to five decimal places.)
Find the second Taylor polynomial T2(x) for the function f(x) = sin(x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-0.8, 0.8]. True or False? |f(x) - T2(x)| ≤ 0.8^3/3! for every x in I. True. False.
Find the second Taylor polynomial T2(x) for the function f(x) = e^x/4 based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval [-1, 1]. True or false: The Quadratic Approximation Error Bound indicates that |f(x) - T2(x)| ≤ 0.001672 for all x in I. True False
Find the second Taylor polynomial T2(x) for the function f(x) = cos(x) based at b = π/6. T2(x) = Let a be a positive real number and let J be the closed interval [π/6 - a, π/6 + a]. Use the Quadratic Approximation Error Bound to verify that |f(x) - T2(x)| ≤ a^3/3! for all x in J. Use this error bound to find a value of a so that |f(x) - T2(x)| ≤ 0.01 for all x in J. (Round your answer to six decimal places.) a =