In: Statistics and Probability
Medical examiners use temperatures of dead bodies to estimate time of death. This is especially important if a crime is suspected. Could the body be reheated to disguise the time of death? A biologist tested this issue in 1951 using mice. He studied the difference (reheated – freshly killed) in the cooling constants of each of the mice.
a) Why is this a paired differences study?
b) Write the hypotheses.
c) Fill in the third column and enter that into your calculator
Freshly Killed | Reheated | Difference |
573 | 481 | |
482 | 343 | |
377 | 383 | |
390 | 380 | |
535 | 454 | |
414 | 425 | |
438 | 393 | |
410 | 435 | |
418 | 422 | |
368 | 346 | |
445 | 443 | |
383 | 342 | |
391 | 378 | |
410 | 402 | |
433 | 400 | |
405 | 360 | |
340 | 373 | |
328 | 373 | |
400 | 412 |
[d] Using a 99% confidence interval for the mean difference in cooling constants, determine if there is significant evidence that reheating the bodies changes the cooling constant. (Remember that you just have one sample. Choose the Data option.)
[e] Calculate the P-value. Does a conclusion from the P-value strengthen or call into question your conclusion from the confidence interval? Explain. (Think about what you will use as the “unusual sample” threshold.)
a) Since ,We have two samples that are dependent on each other.
b) Null hypothesis:
vs
Alternative hypothesis
c)
Freshly Killed | Reheated | Difference |
573 | 481 | -92 |
482 | 343 | -139 |
377 | 383 | 6 |
390 | 380 | -10 |
535 | 454 | -81 |
414 | 425 | 11 |
438 | 393 | -45 |
410 | 435 | 25 |
418 | 422 | 4 |
368 | 346 | -22 |
445 | 443 | -2 |
383 | 342 | -41 |
391 | 378 | -13 |
410 | 402 | -8 |
433 | 400 | -33 |
405 | 360 | -45 |
340 | 373 | 33 |
328 | 373 | 45 |
400 | 412 | 12 |
(d) Degree of freedom =n-1 = 19-1 = 18
t critical value for 99% confidence level is 2.8784
(e)
P value is 0.064
TDIST(-1.98,18,2)................using Excel command for p value
P value 0.064 > 0.01
We fail to reject H0.