Answer to Question #314429 in Statistics and Probability for Rahul

Question

The purpose of a study by Lugli_e et al. (A-5) was to investigate the oral

status of a group of patients

diagnosed with thalassemia major (TM). One of the outcome measures was

the decayed, missing, and

filled teeth index (DMFT). In a sample of 18 patients the mean DMFT index

value was 10.3 with a

standard deviation of 7.3. Is this sufficient evidence to allow us to conclude

that the mean DMFT

index is greater than 9.0 in a population of similar subjects? Let alpha = 0.1

Answer 1

$H_0:\mu \leqslant 9\\H_1:\mu >9\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{18}\frac{10.3-9}{7.3}=0.755539\sim t_{n-1}=t_{17}\\P-value\\P\left( T>0.755539 \right) =F_{t,17}\left( -0.755539 \right) =0.2301$

Since the P-value is greater than the significance level, the null hypothesis is not rejected. There is no evidence that the mean value is greater than 9.