Question

There is evidence that cytotoxic T lymphocytes (T cells) participate in controlling tumor growth and that they can be harnessed to use the body's immune system to treat cancer. One study investigated the use of a T cell-engaging antibody, blinatumomab, to recruit T cells to control tumor growth. Given are the T cell counts (1000 per microliter) at baseline (beginning of the study) and after 20 days on blinatumomab for six subjects in the study. The difference, after 20 days minus baseline, is the response variable. Baseline After 20 days Difference 0.04 0.28 0.24 0.02 0.47 0.45 0.00 1.30 1.30 0.02 0.38 0.33 0.25 1.22 0.44 0.23 0.84 0.11 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV Crunchlt! Do the data give evidence at the 2% level that the mean count of T cells is higher after 20 days on blinatumomab? Answer each question to help determine this. STATE: Will blinatumomab help cancer patients recruit T cells? PLAN: Let y represent the mean increase in T cell counts after 20 days of blinatumomab. Select the correct hypotheses we will test. O Ho:u=0 versus Ha! > 20 OH : #0 versus H,:u= 0 O Ho:u= 0 versus H,:< OHH = versus H. > 0 O Ho:u=0 versus H: 80 SOLVE: Find X, and 1. (Enter your answer for rounded to four decimal places, and your answer for rounded to three decimal places.) Using software, find the P-value. (Enter your answer rounded to four decimal places.) CONCLUDE: Does the data give evidence at the 2% level that the mean count of T cells is higher after 20 days on blinatumomab? O no ves

Answer 1

first part:

mean() =- 0.24 +0.45 + 1.30 +0.23 +0.84+ 0.11 -= 0.5283 Standard deviation(s) = V (0.24 – 0.5283)2 + (0.45 – 0.5283)2 + (1.30 – 0.5283)2 + (0.23 -0.5283)2 + (0.84 – 0.5283)2 + (0.11 – 0.5283)2 6-1 s=0.4574

Ho: p=0 versus Ha: p > 0

Second part:

ī = 0.5283 t=2-4 - 0.5283 s/n 0.4574/V6 = 2.829

degree of freedom =n-1=6-1=5

p-value=P(t>2.829)= 0.0184

here,

p-value < significance(alpha=0.02), reject the null hypothesis.

Ans: Yes