Question

A frequenter of a pub had observed that the new barman poured in average 0.47 liters of beer into the glass with a standard deviation equal to 0.18 liters instead of a half a liter with the same standard deviation. The frequenter had used a random sample of 45 glasses of beer in his experiment. Consider the one-sided hypothesis test for volume of beer in a glass: Ho: 0.5 agaist H1 0.5 Determine the P-value of this test. Round your answer to four decimal places (e.g. 98.7654). P-value the absolute tolerance is +/-0.0001

Answer 1

Solution :

$\mu$= 0.5

$\bar x$ =0.47

$\sigma$ =0.18

n = 45

This is the LEFT tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 0.5

H_a : $\mu$ <0.5

Test statistic = z

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

= (0.47-0.5) / 0.18 / $\sqrt$ 45

= -1.12

P(z <-1.12) = 0.1314

P-value = 0.1314