Question

Brian is a cancer researcher who is trying to develop a new treatment to extend the lives of cancer victims. He knows that the survival rate for the population of people with this type of cancer is 6.4 years. Brian gathers a random sample of people with cancer and gives them his new experimental medication; he then records how long they survive. Using his data below, test the hypothesis that Brian’s new drug increases the length of time people with cancer survive. Be sure to include all necessary elements of your analysis, including hypotheses, calculation of the appropriate statistic, comparison to critical values, decision, and a complete interpretation of your decision.

X	X2
7	49
9	81
6	36
4	16
8	64
8	64
7	49
5	25
9	81
7	49
7	49

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HPOTHESIS Ha:

LEVEL OF SIGNIFICANCE =0.05

Test statistic t= xbar-mean/s/sqrt(n)

t= 7-6.4/1.48/sqrt(11)

t= 0.6/1.48/3.32

t= 0.6/0.446

t= 1.345

degrees of freedom =11-1=10

t critical value= 1.812

Since tcritical value is GREATER THAN t statistic therefore DO NOT REJECT H0.

CONCLUSION: WE DON'T HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT the survival rate for the population of people with this type of cancer is greater than 6.4 years

NOTE: YOU HAVE NOT MENTIONED LEVEL OF SIGNIFICANCE SO I ASSUMED 0.05