Question

In: Statistics and Probability

Medical examiners use temperatures of dead bodies to estimate time of death. This is especially important...

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.)

Solutions

Expert Solution

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.


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