Find the probability mass function of y = 2x + 3 y = x^2. A sample of size 49 wa

Question

Find the probability mass function of y = 2x + 3 y = x^2. A sample of size 49 was drawn from a normally distributed population, and the 99 percentage CI for mu is (-2, 10) Find the sample mean x Find the sample variance s^2 Two scientists claimed that a new treatment is more effective than the standard treatment 4. for prolonging the lives of terminal cancer patients. The standard treatment has been in use for a long time, and from records in medical journals, the mean survival period is known to be 4.2 years. The new treatment is administered to 25 patients and their with duration of survival recorded. The mean and the standard deviation for the sample the new treatment are found to be 5.5 and 1.0 years, respectively. Is it really a more effective treatment? Formulate the null and alternative hypotheses for the Find the critical value for significance level alpha =.05. Find the test statistics Draw conclusion

Explanation / Answer

3)a) sample mean =(-2+10)/2 =4

b)here margin of error =(10-(-2))/2 =6

for (n-1=48) degree if freedom and 99% CI, t=2.6822

hence std error =margin of error /t =2.237

from above variance =(std error)2*n =(2.237)2*49 =245.20

4)null hypothesis: mean <=4.2

alternate hypothesis: mean >4.2

b) critical value for 0.05 level and 24 df =1.7109

c) here std error =std deviation/(n)1/2=0.2

hence test stat t=(X-mean)/std error =(5.5-4.2)/0.2=6.5

d) as test stat is higher then critical value, hence we reject null hypothesis and conclude that new treatment is bbetter

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