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. Question 37 You wish to determine if there is a linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.01 and round all values to 4 decimal places. Driver Age |Number of Driver Deaths per 100,000 4 29 67 30 59 24 74 31 40 27 68 19 50 18 45 23 77 35 45 27 Ho: p = 0 Ha: p = 0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is O Less than (or equal to) o O Greater than o The p-value leads to a decision to O Accept Ho O Do Not Reject Ho O Reject Ho The conclusion is O There is a significant positive linear correlation between driver age and number of driver deaths. There is a significant negative linear correlation between driver age and number of driver deaths. O There is a significant linear correlation between driver age and number of driver deaths. There is insufficient evidence to make a conclusion about the linear correlation between driver age and number of driver deaths.Question 33 What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time 16 10 16 15 10 16 4 Score 88 90 96 100 83 94 59 62 a. Find the correlation coefficient: T = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: 2v = 0 0 The p-value is: (Round to four decimal places) C. Use a level of significance of o = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful. There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. O There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate. O There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. d. p' = (Round to two decimal places) e. Interpret p2 : 85% of all students will receive the average score on the final exam. O Given any group that spends a fixed amount of time studying per week, 85% of all of those students will receive the predicted score on the final exam. O There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 85%. O There is a 85%% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. f. The equation of the linear regression line is: y = I (Please show your answers to two decimal places) g. Use the model to predict the final exam score for a student who spends 10 hours per week studying. Final exam score = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: O The slope has no practical meaning since you cannot predict what any individual student will score on the final. O For every additional hour per week students spend studying, they tend to score on averge 2.41 higher on the final exam. O As x goes up, y goes up. i. Interpret the y-intercept in the context of the question: O The average final exam score is predicted to be 57. O The y-intercept has no practical meaning for this study. If a student does not study at all, then that student will score 57 on the final exam. O The best prediction for a student who doesn't study at all is that the student will score 57 on the final exam.Question 32 16%% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who live in the inner city have sleep apnea. Of the 387 people from the inner city surveyed, 74 of them suffered from sleep apnea. What can be concluded at the level of significance of o = 0.05? a. For this study, we should use | Select an answer b. The null and alternative hypotheses would be: Ho: [? | Select an answer V (please enter a decimal) H, : 7 v Select an answer V Please enter a decimal) C. The test statistic [? v ] = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) 2. The p-value is ? vo f. Based on this, we should | Select an answer w | the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly larger than 16% at o = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 16%. The data suggest the populaton proportion is significantly larger than 16% at or = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 16k O The data suggest the population proportion is not significantly larger than 16% at o = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 16%. h. Interpret the p-value in the context of the study. O There is a 4.7% chance of a Type I error. O If the population proportion of inner city residents who have sleep apnea is 16% and if another 387 inner city residents are surveyed then there would be a 4.7% chance that more than 19% of the 387 inner city residents surveyed have sleep apnea. There is a 4.7% chance that more than 16% of all inner city residents have sleep apnea. O If the sample proportion of inner city residents who have sleep apnea is 19% and if another 387 inner city residents are surveyed then there would be a 4.7% chance of concluding that more than 16% of all inner city residents have sleep apnea. i. Interpret the level of significance in the context of the study. If the population proportion of inner city residents who have sleep apnea is larger than 16% and if another 387 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 16%. O There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth. There is a 5% chance that the proportion of all inner city residents who have sleep apnea is larger than 16%. O If the population proportion of inner city residents who have sleep apnea is 16% and if another 387 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is larger than 16.Question 31 It takes an average of 11.7 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will change if the patient is immediately told the truth about the injury. The EMT randomly selected 67 injured patients to immediately tell the truth about the injury and noticed that they averaged 11.1 minutes for their blood to begin clotting after their injury. Their standard deviation was 1.47 minutes. What can be concluded at the the o = 0.05 level of significance? a. For this study, we should use | z-test for a population proportion V b. The null and alternative hypotheses would be: Ho: Hyll 11.1 HI: HVE 11.1 C. The test statistic [E v | = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is > va f. Based on this, we should |fail to reject the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population mean is not significantly different from 11.7 at o = 0.05, so there is statistically significant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is equal to 11.7. O The data suggest that the population mean is not significantly different from 11.7 at o = 0.05, so there is statistically insignificant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is different from 11.7. The data suggest the population mean is significantly different from 11.7 at o = 0.05, so there is statistically significant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is different from 11.7.. Question 28 You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 16%. You would like to be 98% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required? Hint: Video & [+] n =. Question 27 A smart phone manufacturer is interested in constructing a 99% confidence interval for the proportion of smart phones that break before the warranty expires. 89 of the 1520 randomly selected smart phones broke before the warranty expired. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all smart phones that break before the warranty expires is between and b. If many groups of 1520 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about percent will not contain the true population proportion. Hint: Hints Video & [+] Submit Question. Question 25 You are interested in finding a 95% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 15 randomly selected college students. Round answers to 3 decimal places where possible. 11 5 3 1 10 12 12 5 16 1 1 0 11 7 a. To compute the confidence interval use a [? v | distribution. b. With 95% confidence the population mean number of days of class that college students miss is between and days. c. If many groups of 15 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of missed class days and about percent will not contain the true population mean number of missed class days. Hint: Hints Video & [+] Submit Question. Question 22 Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1 month. 14 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. What is the distribution of ? E - N C. What is the probability that one randomly selected person learned to walk when the person was between 10.5 and 12.5 months old? d. For the 14 people, find the probability that the average age that they learned to walk is between 10.5 and 12.5 months old. e. For part d), is the assumption that the distribution is normal necessary? O Yes No f. Find the IQR for the average first time walking age for groups of 14 people. Q1 = months Q3 = months IQR: months
