Kidney stones are small, solid mineral deposits inside kidneys, and they cause s
ID: 3228001 • Letter: K
Question
Kidney stones are small, solid mineral deposits inside kidneys, and they cause sharp pains. In 1986, a research team (Charig, Webb, Payne and Wickham) presented data which compare the success probabilities of two treatments for kidney stones. We consider two main procedures, open procedures (Treatment A) and percutaneous nephrolithotomy (Treatment B). Treatment A is commonly used for large stones, and Treatment B (removing stones by a small puncture wound through the skin) is commonly used for small stones. The explanatory variable is the treatment (Treatment A or B), and the response variable is the outcome of the treatment (success or failure), so both variables are categorical. Here is the summary of the data. We want to test whether one treatment is superior to the other treatment at alpha = 0.05. a. State the null hypothesis H_0 and the alternative hypothesis H_1 in words. b. If H_0 is true, what is the estimated marginal probability of success? c. Complete the table of expected counts. d. Calculate the test statistic T without using R. Show your work.Explanation / Answer
a)
H0: 1 – 2 = 0 (Both treatments are similar)
H1: 1 – 2 0 (One of the treatments is superior)
b)
Estimated marginal probability of success is 562/700=0.80
c)
d)
x^2STAT=(fo-fe)^2/fe=(273-280)^2/280....+(61-70)^2/70=2.32
Treatment A Treatment B Total Success 280 280 560 Failure 70 70 140 Total 350 350 700d)
x^2STAT=(fo-fe)^2/fe=(273-280)^2/280....+(61-70)^2/70=2.32
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