The equation of motion of a particle is s = t3 − 12t, where s is in meters and t is in seconds. (Assume t ≥ 0.) (a) Find the velocity and acceleration as functions of t. v(t) = a(t) = (b) Find the acceleration after 6 s. m/s2 (c) Find the acceleration when the velocity is 0. m/s2

InstructionsIf the question requires computation, do the calculations and then give or select the correct values using the following rule:Keep at least 4 decimal places at intermediate steps of a calculation, and round your final answer to 2 decimal places, unless otherwise noted. For example: 16.6667 would become 16.67 after rounding(In the course notes for Module 7, probabilities such .678934 are instead rounded to four decimal places, so the correct way to report the aforementioned probability is .6789)Multiple AttemptsForce CompletionQuestion 1The following 5 questions (Q1 to Q5) are based on the following example:A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6. The appropriate statistical procedure for this example would be az-testt-testQuestion 2A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6. Is this a one-tailed or a two-tailed test?one-tailedtwo-tailedQuestion 3A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6. The most appropriate null hypothesis (in words) would beThere is a statistical difference in the amount of empathy expressed when comparing individuals who were bullied to the general population.There is no statistical difference in the amount of empathy expressed when comparing individuals who were bullied to the general population.Being bullied does significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.Being bullied does not significantly increase empathy when compared to the population of individuals in the general population who have not been bullied.Question 4A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6. The most appropriate null hypothesis (in symbols) would beμempathy = 39.5μempathy = 30.6μempathy > 39.5μempathy > 30.6Question 5A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6.Test at the .05 level of significance.Set up the criteria for making a decision. That is, find the critical value using analpha = .05. (Make sure you are sign specific: + ; - ; or ± ) (Use your tables)-1.645±1.645±2.7562.064±2.064Question 6A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 116 scores obtained from individuals who were bullied yielded a mean of 39.5 and a standard deviation of 6.6. (Use these numbers only for this question!) What are the degrees of freedom? (numeric value only) Question 7A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 59.39. Random sampling of 51 scores obtained from individuals who were bullied yielded a mean of 54.72 and a standard deviation of 8.69. (Use these numbers only for this question!) What is the z-value or t-value you obtained (your test statistic)? (numeric value only, including negative sign if required)Question 8A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6.Test at the .05 level of significance.Suppose that the value of your calculated (obtained) test statistic is 6.74. What is your decision?reject the null hypothesisfail to reject the null hypothesisreject the alternative hypothesisQuestion 9A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6.Test at the .05 level of significance.The best conclusion for this example (based on your answer to Q8) would beBeing bullied does not significantly increase the amount of empathy expressed by individuals who were bullied when compared to the general population.Being bullied does not significantly decrease the amount of empathy expressed by individuals who were bullied when compared to the general population.There is no statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.There is a statistical difference in the amount of empathy expressed by individuals who were bullied when compared to the general population.Question 10A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6.Test at the .05 level of significance.Based on your evaluation of the null in Q8 and your conclusion is Q9, as a researcher you would be more concerned with aType I statistical errorType II statistical errorQuestion 11A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 61.23. Random sampling of 76 scores obtained from individuals who were bullied yielded a mean of 44.07 and a standard deviation of 22.87. (Use these numbers only for this question!) Suppose you want to calculate the 99% confidence interval.The mean you will use for this calculation is:Question 12A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. Random sampling of 25 scores obtained from individuals who were bullied yielded a sample mean of 39.5 and a sample standard deviation of 6.6.Suppose you want to calculate the 99% confidence interval.What is the new critical value you will use for this calculation?±1.645±2.064±2.756±2.7976.74Question 13A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 65.49. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 61 and a standard deviation of 20.11. (Use these numbers only for this question!) Calculate the 99% confidence interval. Steps: As you know, two values will be required to complete the following equation: _________ ≤ µ ≤ __________ For this question, what is the value that is below or less than µ?Question 14A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 57.14. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 69.38 and a standard deviation of 8.91. (Use these numbers only for this question!) Calculate the 99% confidence interval. Steps: As you know, two values will be required to complete the following equation: _________ ≤ µ ≤ __________ For this question, what is the value that is above or greater than µ?Question 15If α = 0.14, and β = 0.05, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only) The statistical decision is to reject the null, and H0 is really true (i.e., a Type I error)Question 16If α = 0.06, and β = 0.09, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only) The statistical decision is to fail to reject null, and H0 is really true (i.e., a correct decision)Question 17If α = 0.15, and β = 0.16, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only) The statistical decision is to reject the null, and H0 is really false (i.e., Power)Question 18If α = 0.07, and β = 0.14, complete the following questions by inserting the appropriate probability of each. (Response must be in decimal form) (Use these values for this question only) The statistical decision is to fail to reject the null, and H0 is really false (i.e., a Type II error)Question 19A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?The appropriate statistical procedure for this example would be a:t-testz-testchi-square goodness of fitchi-square test for independenceQuestion 20A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? Is this a one-tailed or a two-tailed test?one-tailedtwo-tailedQuestion 21A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? The most appropriate alternative hypothesis (in words) would be:There is no significant difference in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.There is a significant increase in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.People taking Atenolol will not experience a significantly lower systolic blood pressure when compared to the general population of people who do not take Atenolol.People taking Atenolol will experience a significantly lower systolic blood pressure when compared to the general population of people who do not take Atenolol.Question 22A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? The most appropriate alternative hypothesis (in symbols) would be:µBloodPressure = 165µBloodPressure = 147µBloodPressure < 165µBloodPressure< 147Question 23A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? Set alpha equal to .01. Set up the criteria for making a decision. That is, find the critical value using an alpha = .01. (Make sure you are sign specific: + ; - ; or +/-) (Use your tables)+/- 2.457- 2.462- 2.750+/- 2.756Question 24A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The 114 individuals who take Atenolol have an average systolic blood pressure of 147, with a sample standard deviation of 11.89. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) What is the numeric value of your standard error? Question 25A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 162 (µ = 162). The 167 individuals who take Atenolol have an average systolic blood pressure of 121, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) What is the z-value or t-value you obtained (your test statistic)? (numeric value only, including negative sign if required) Question 26A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? Set alpha equal to .01. Suppose that the value of your calculated (obtained) test statistic is -16.51. What is your decision?Reject the null hypothesisFail to reject the null hypothesisQuestion 27A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? Set alpha equal to .01. The best conclusion for this example (based on your answer to Q26) would be:There is no significant difference in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.There is a significant difference in systolic blood pressure when comparing people who take Atenolol to the general population of people who do not take Atenolol.People taking Atenolol did not experience a significantly lower systolic blood pressure when compared to the general population of people who do not take Atenolol.People taking Atenolol experienced a significantly higher systolic blood pressure when compared to the general population of people who do not take Atenolol.Question 28A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? Set alpha equal to .01. Based on whether you rejected or failed to reject the null hypothesis (Q26), and your conclusion in Q27, as a researcher, you would be more concerned with a:Type I statistical errorType II statistical errorQuestion 29A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The 30 individuals who take Atenolol have an average systolic blood pressure of 179, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these data for this question only!) Calculate the 95% confidence interval The mean you will use for this calculation is: Question 30A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The sample of 30 individuals who take Atenolol have an average (mean) systolic blood pressure of 147, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?Calculate the 95% confidence intervalWhat is the new critical value you will use for this calculation?+/- 1.699+/- 2.045+/- 2.457+/- 2.462- 2.045Question 31A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 150 (µ = 150). The 30 individuals who take Atenolol have an average systolic blood pressure of 167, with a sample standard deviation of 14. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% confidence interval As you know, two values will be required to complete the following equation: _________ ≤ µ ≤ __________ For this question, what is the value that is below or less than µ? Question 32A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 156 (µ = 156). The 30 individuals who take Atenolol have an average systolic blood pressure of 159, with a sample standard deviation of 23. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% confidence interval As you know, two values will be required to complete the following equation: _________ ≤ µ ≤ __________ For this question, what is the value that is above or greater than µ? A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 156 (µ = 156). The 30 individuals who take Atenolol have an average systolic blood pressure of 159, with a sample standard deviation of 23. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure? (Use these numbers only for this question!) Calculate the 95% confidence interval As you know, two values will be required to complete the following equation: _________ ≤ µ ≤ __________ For this question, what is the value that is above or greater than µ? Question 33The average time scheduled for a doctor’s visit is 17 minutes with a standard deviation of 14 minutes. A researcher uses a sampling distribution made up of samples of size 92. (Use these numbers for this question only!) According to the Central Limit Theorem, what is the standard error of the mean?Question 34The average time scheduled for a doctor’s visit is 9 minutes with a standard deviation of 8 minutes. A researcher uses a sampling distribution made up of samples of size 152. (Use these numbers for this question only!) According to the Central Limit Theorem, what is the mean of the sampling distribution of means?Question 35Which of the following is most likely to increase the calculated value of a t-test?Increase the number of subjectsDecrease the number of subjectsRepeat with a convenience sampleRepeat with the same sampleRepeat with a stratified random sampleQuestion 36As you increase the true distance between the null and alternative hypotheses, the likelihood of rejecting the null hypothesisIncreasesDecreasesRemains the sameQuestion 37Keeping everything else the same, if you were to change your alpha level from .01 to .05, the likelihood of rejecting the null hypothesisIncreasesDecreasesRemains the sameQuestion 38In a research setting, it is more common to use t-tests than z-tests becauseTypically the population mean is unknown.Typically the population standard deviation is unknown.They are more accurate since sample size is taken into account when determining critical values.Typically the sample mean is unknown."t" comes before "z" in the alphabetQuestion 39What is the basic question that underlies hypothesis testing?Is the sample representative of the population?Could the relationship observed in the sample have occurred by chance?What is the standard score?Should we reject the null hypothesis?