Question

A medical researcher maintains that the mean hemoglobin reading of surgical patients is different from 12 grams per deciliter. He randomly selects nine surgical patients and obtains the following data:

8.8

12.5

10.3

12.0

14.6

9.1

9.9

13.0

14.6

1. What conditions must be met in order to use the T-Test?
2. Are the conditions met? Explain.
3. If the conditions are met, perform the test by writing the null and alternative hypothesis, finding the p-value, making a decision and offering a conclusion if the level of significance is 0.01.
4. If the conditions are not met, what should be done?

Answer 1

a. Condition : data should come from the normal distribution

b. Yes. Since we check the normality by Shapiro test in R

R code:

x<-c(3,8.8,9.1,9.9,10.,12,12.5,13,14.6,14.6)
shapiro.test(x)
hist(x,main="Main",xlab="value",border="light blue",col="blue",las=1)

Since, p-value=0.199663>α=0.05, we accept the H0.
It is assumed that the data is normally distributed..

c. Ho: vs H1:​​​​​​