A PROMINENT PSYCHOLOGIST AT A NEW YORK HOSPITAL CLAIMS THAT A NEW FORM OF PSYCHOTHERAPY FOR A CERTAIN TYPE OF MENTAL DISORDER WILL HELP A PATIENT TO BE READY FOR OUTPATIENT TREATMENT IN AN AVERAGE OF $12$ WEEKS. A RESIDENT PSYCHOLOGIST DECIDES TO TEST THIS CLAIM UNDER THE SUSPICION THAT THE CLAIM IS TOO LOW. THE RESIDENT PSYCHOLOGIST USES THIS NEW FORM OF PSYCHOTHERAPY ON A RANDOM SAMPLE OF $40$ PATIENTS. THE TIME REQUIRED FOR THESE PATIENTS TO REACH OUTPATIENT STATUS WERE $($IN DAYS$)$:

$91,88,86,95,90,93,87,89,83,91,93,86,92,91,90,83,92,88,90,93,87,94,86,84,92,87,85,$

$90,88,84,92,94,86,91,89,84,89,85,95.$ DO THES SAMPLE DATA SUPPORT THE CLAIM MADE BY THE RESIDENT

PSYCHOLOGIST AT ALPHA $=1\%$

BUTTERFLY WINGS: DO LARGER BUTTERFLYS LIVE LONGER

WINGSPAN IN MILLIMETERS, LIFESPAN IN DAYS

WINGSPAN

$35\mathrm{.}50$

$30\mathrm{.}60$

$30\mathrm{.}00$

$32\mathrm{.}30$

$23\mathrm{.}90$

$27\mathrm{.}70$

$28\mathrm{.}80$

$35\mathrm{.}90$

$25\mathrm{.}40$

$24\mathrm{.}60$

$28\mathrm{.}10$

$25\mathrm{.}90$

$31\mathrm{.}30$

$23\mathrm{.}00$

$26\mathrm{.}30$

$23\mathrm{.}70$

$27\mathrm{.}10$

$28\mathrm{.}10$

$25\mathrm{.}90$

$28\mathrm{.}80$

$31,40$

$28\mathrm{.}50$

Y

LIFESPAN

$19\mathrm{.}80$

$17\mathrm{.}30$

$27\mathrm{.}50$

$22\mathrm{.}40$

$40\mathrm{.}70$

$18\mathrm{.}30$

$25\mathrm{.}90$

$23\mathrm{.}10$

$24\mathrm{.}00$

$38\mathrm{.}80$

$36\mathrm{.}50$

$32\mathrm{.}50$

$27\mathrm{.}50$

$31\mathrm{.}00$

$37\mathrm{.}40$

$22\mathrm{.}60$

$23\mathrm{.}10$

$18\mathrm{.}50$

$32\mathrm{.}30$

$29\mathrm{.}10$

$37\mathrm{.}00$

$33\mathrm{.}70$

THERE ARE $22$ SPECIES, ALL IN $1$ PROBLEM

IS THERE A NEGATIVE

LINEAR CORRELATION?

LINEAR REGRESSION

LIN REG TTEST

SCATTERGRAM