Question

Consider H0: μ=72 versus H1: μ>72. A random sample of 16 observations taken from this population produced a sample mean of 75.4. The population is normally distributed with σ=6.

a. Calculate the p-value. Round your answer to four decimal places.

Answer 1

Solution :

$\mu$= 72

$\bar x$ =75.4

$\sigma$ =6

n = 16

This is the RIGHT TAIL TEST

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 75

H_a : $\mu$ > 75

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (75.4-72) /6 / $\sqrt$ 16

= 2.27

P(z > 2.27) = 1 - P(z < 2.27 ) = 1-0.9884=0.0116

P-value = 0.0116