One of the methods forensic investigators use for estimating the age at death of a human, or the age of a living individual (for example for legal reasons or to verify identity) is based on measurement of the biochemical changes in amino acids within the teeth or bones. As bones and teeth age the ratioof two amino acids, denoted simply as R and L, increases. The biochemical changes that occur over time in these amino acids follow an exponential law. The age t, in years, can be estimated fromusing the equation t = b₀+ b₁*LN, where LN denotes the natural logarithm (logarithm base e).

ThisExcel filehas data on the ratiofrom the teeth of human subjects of known age.

Question 1. Use the data to find the least squares intercept b₀and slope b₁in the equation t = b₀+ b₁*LN.

intercept b_0-26.72

slope b_1808.65

Question 2. While tending to his flower garden, Sherlock Holmes discovers a body buried in his backyard. Forensic analysis yields the value 0.045 for the ratio. Use the least squares equation to estimate the age of Sherlock Holmes' surprise garden visitor.

years

46.1

Question 3. Calculate a 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor.

lower bound- need answer to this

upper bound-need answer to this

Question 4. Several years ago a man in Sherlock Holmes's neighborhood mysteriously disappeared. At the time of the disappearance the man was 35 years old. Do you think that this is the body of that man?

YesNo

2.The SAT and ACT are the two major standardized tests that colleges use to evaluate applicants. Most students take just one of these tests. However, some students take both. This Excel file gives the scores of 60 students who took both tests. Can we relate the two tests? Plot the data with SAT on the x axis and ACT on the y axis and answer the questions below. Question 1. Find the slope and intercept of the least squares regression line (draw the least squares line on your plot). 1.62 Correct: Your answer is correct. intercept (use 4 decimal places) 0.0214 Correct: Your answer is correct. slope (use 4 decimal places) Question 2. Give the value of the test statistic for a test of H0: 1 = 0. 0.995 Incorrect: Your answer is incorrect. (use 4 decimal places) Question 3. If the alternative hypothesis is Ha: 1 0, what is the rejection region if the significance level of the test is = .05? Use this t-table to determine your answer. t -2 Correct: Your answer is correct. t 2 Correct: Your answer is correct. Question 4. What is the correct conclusion for this hypothesis test? Reject the null hypothesis H0 and conclude that in a linear model SAT score is useful for predicting the ACT score. Do not reject the null hypothesis H0; the SAT score is not useful for predicting the ACT score. Correct: Your answer is correct. Question 5. Determine a 95% confidence interval for the slope 1 of the least squares line (use 3 decimal places in your answers; use this t-table to determine the correct t-value). 0.0128 Incorrect: Your answer is incorrect. lower endpoint of confidence interval upper endpoint of confidence interval