hese are previous year papers that i want to solve before the start of next semester. Can you please help me solve these? A new drug has been developed to treat cancer. It is of interest to know whether the low dose (X1 = 0) or high dose (X1 = 1) will be better for cancer patients. There are 60% of patients randomly assigned to high dose. For this question, if asked to do a hypothesis test, please include the following: 1. The formula of the test statistic, 2. the reference distribution with degrees of freedom and the conditions for the test statistic to follow this reference distribution, 3. plug in the numbers from the R output into the test statistic. You do not need to simplify the expression, 4. state when will you reject or fail to reject the hypothesis.
These are previous year papers that i want to solve before the start of next semester. Can you please help me solve these?
A new drug has been developed to treat cancer. It is of interest to know whether the low dose (X1 = 0) or high dose (X1 = 1) will be better for cancer patients. There are 60% of patients randomly assigned to high dose.
For this question, if asked to do a hypothesis test, please include the following:
1. The formula of the test statistic,
2. the reference distribution with degrees of freedom and the conditions for the test statistic
to follow this reference distribution,
3. plug in the numbers from the R output into the test statistic. You do not need to simplify
the expression,
4. state when will you reject or fail to reject the hypothesis.
a)Write out the linear regression model of Y (a continuous measure of tumor size) on dose X1 using low dose as reference level.
b) The r output of the regression model from part 1 is given below. Fill in the blanks.
Call:
lm(formula = Y ~ X1)
Residuals:
Min 1Q
-3.3091 -0.8803 0.0035 0.5994 2.6593
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.0375 _____ 6.031 2.89e-08 ***
X1 -0.2084 _____ -0.938 0.35
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 1.088 on 98 degrees of freedom
Multiple R-squared: 0.008905,Adjusted R-squared: -0.001209
F-statistic: 0.8805 on _____ and ______ DF, p-value: ___________
c) The investigator tells you that gender X2 is also an important factor on the tumor size. The model include both X1 and X2 are given below. Fill in the blanks.
> mean(Y[X1==0&X2==0])
[1] 0.793014
> mean(Y[X1==0&X2==1])
[1] 2.015229
> mean(Y[X1==1&X2==1])
[1] 1.728358
> mean(Y[X1==1&X2==0])
[1] 0.5553849
Call:
lm(formula = Y ~ X1 + X2 + X1 * X2)
Residuals:
Min 1Q Median 3Q Max
-3.0354 -0.7025 0.1240 0.5758 2.2696
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) _________ 0.17274 4.591 1.34e-05 ***
X1 _________ 0.22493 -1.056 0.29341
X2 _________ 0.38625 3.164 0.00208 **
X1:X2 _________ 0.48800 -0.101 0.91984
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 0.9771 on ___ degrees of freedom
Multiple R-squared: 0.2168,Adjusted R-squared: 0.1923
F-statistic: 8.857 on ____ and ____ DF, p-value: 3.062e-05
d) Consider the following model (a is alpha and e is epsilon)
Y = a11(X1 = 0;X2 = 0)+a21(X1 = 0;X2 = 1)+a31(X1 = 1;X2 = 0)+a41(X1 = 1;X2 = 1)+e
Test the hypothesis
-> H0 : a1 - a2 = a3 - a4 vs Hb : a1 -a2 is not equal to a3 - a4
-> H0 : a1 - a2 = a3 - a4 = 0 vs Hb : a1 - a2 is not equal to 0 or a3 - a4 is not equal to 0
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