Answer to Question #197808 in Statistics and Probability for MARY ANN YATONG

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.