Question

9, 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 32, the p-value is

Answer 1

Q.9) Given that, sample size ( n ) = 32

sample mean $(\bar x)$ = 70

population variance $(\sigma^2)$ = 400

population standard deviation $(\sigma) = \sqrt { 400} = 20$

The null and the alternative hypotheses are,

$H_0: \mu = 80 \text { versus } H_1: \mu < 80$

Test statistic is,

$Z = \frac { 70-80}{\frac { 20}{\sqrt { 32}}}= -2.83$

Since, it is left-tailed test,

p-value = P(Z < -2.83) = 0.0023

p-value = 0.0023