Answer to Question #314433 in Statistics and Probability for Rahul

Question

Nine laboratory animals were infected with a certain bacterium and then

immunosuppressed. The

mean number of organisms later recovered from tissue specimens was 6.5

(coded data) with a

standard deviation of .6. Can one conclude from these data that the

population mean is greater than 6?

Let alpha = 0.5What assumptions are necessary?

Answer 1

$H_0:\mu \leqslant 6\\H_1:\mu >6\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{9}\frac{6.5-6}{0.6}=2.5\sim t_{n-1}=t_8\\P\left( T>2.5 \right) =F_{t,8}\left( -2.5 \right) =0.0185$

Since the P-value is less than the significance level, the null hypothesis is rejected. The

population mean is greater than 6. We assume normal distribution.