use calculator method please **Title: Genetic Engineering for Cancer Treatment****Overview:**This section continues the discussion on genetic engineering for cancer treatment. Specifically, it focuses on an experimental study measuring the presence of cells that induce an immune response in the body, which might help in fighting cancer.**Data Presentation:**The data comprises counts of active cells per 100,000 cells for 11 subjects, recorded before and after the infusion of modified cells. The table displays these values:| Subject | Before | After | Difference (After - Before) ||---------|--------|-------|-----------------------------|| 1 | 14 | 41 | 27 || 2 | 0 | 7 | 7 || 3 | 1 | 1 | 0 || 4 | 0 | 215 | 215 || 5 | 0 | 20 | 20 || 6 | 0 | 700 | 700 || 7 | 0 | 13 | 13 || 8 | 0 | 530 | 530 || 9 | 20 | 35 | 15 || 10 | 1 | 92 | 91 || 11 | 6 | 108 | 102 |**Discussion:**- **(a)** Explain why this is a matched pairs design.- **(b)** Examine the data. Is it reasonable to use the t procedures?- **(c)** If your conclusion in part (b) is Yes, do the data give convincing evidence that the count of active cells is higher after treatment?In this experiment, the matched pairs design allows for each subject to serve as their own control, comparing the before and after measurements to isolate the effect of the treatment. Statistical procedures, such as the t-test, may be applicable to determine the significance of the observed differences. The outcomes potentially provide evidence of increased active cell counts following treatment, supporting the hypothesis that genetic engineering can enhance immune responses in the context of cancer treatment.

Name: use calculator method please **Title: Genetic Engineering for Cancer T
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: use calculator method please **Title: Genetic Engineering for Cancer Treatment****Overview:**This section continues the discussion on genetic engineering for cancer treatment. Specifically, it focuses on an experimental study measuring the presence o

(a). In this situation, data is obtained from same units before and after infusion of the modified cells. that is observation after the infusion is related to the observation before infusion. therefore, it is a matched pairs design. b). The data collected for 11 subjects sample size is n = 11 which is less than 30 that is the sample is a small sample and population standard deviation is unknown therefore, clearly t distribution is used, final answer is 'Yes'(c). let us assume μ1 be the mean of count of active cells after treatment. μ2 be the mean of count of active cells before treatment. Null hypothesis H0: The data do not give convincing evidence that the count of active cells is higher after treatment. clearly, there is no significant difference between in the count of active cells before and after the treatment. i.e. μ1 = μ2 Alternative hypothesis Ha: The data give convincing evidence that the count of active cells is higher after treatment. i.e. μ1 > μ2 Since the test is a paired t-test, consider the difference values as a single sample. let it be denoted by 'd' Values of d : 27, 7, 0, 215, 20, 700, 13, 510, 34, 86, 108 n = 11, ∑d111 = 1720, ∑d2111 = 817888 d = 1n∑d111 = 172011 = 156.3636 s = 1n∑d2111 -d2 = 111(817888) - (156.3636)2 = 74353.4545 - 24449.5754 = 49903.8791 = 223.39176 Test statistic is given by t = dsn = 156.3636223.3917611 = 156.363667.35515 = 2.3215 Here t statistic follows t-distribution with (n - 1) degrees of freedom Critical value of t at 5% level of significance for (n - 1) = (11 - 1) = 10 d.f is 1.81 can be obtained by using critical value of t-distribution table. Conclusion: The computed value of test statistic = 2.3215 is greater than critical value 1.81 therefore, reject null hypothesis H0 that is you can conclude that the data give convincing evidence that the count of active cells is higher after treatment.