Question

The processors of Peanut's Butter indicate on the label that the bottle contains 16 ounces of peanuts. The standard deviation of the process is 0.5 ounces. A sample of 36 bottles from the last hour's production revealed a mean weight of 16.12 ounces per bottles, at the α = 0.05 is the process out of control? That is, can we conclude that the mean amount per bottle is different from 16 ounces. Find the critical value?

Answer 1

We have given that,

$\mu = 16$

$\sigma = 0.5$

$n = 36$

$\bar x = 16.12$

$\alpha= 0.05$

$H_0: \mu_0 = 16$

$H_0 : \mu_0 \ne 16$

Applying z test,

$z = \dfrac{16.12-16}{\dfrac{0.5}{\sqrt{36}}}$

$z = \dfrac{0.12}{0.083}$ ; $z = 1.44$

We know that value of $z$ at 0.05 level of significance the critical value $=\pm 1.96$

Hence, our calculated value is less than te absolute value of $z_{\alpha}$ .

Therefore, Null Hypothesis is verified.