Question

1. A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70. Consider the null hypothesis Ho: µ = 80 versus the alternative H1: Ho: µ < 80. Compute the p-value. If n = 16, the p-value is ?

Answer 1

Answer : Given,

Variance ($\sigma ^2$) = 400

=> $\sigma^2$ = (20)^2

=> $\sigma$ (population standard deviation) = 20.

$\sigma$/root over n = 20 / root over 16 = 20 / 4 [ As n = 16]

Now,

P-value = (Sample mean - $\mu$) ÷ ( $\sigma$/root over n )

=> P-value = (70 - 80) ÷ (20/4) = (-10) ÷ 5 = -2

Therefore, p-value is -2.