Answer to Question #288657 in Statistics and Probability for Müg

Question

A particular brand of diet margarine was analyzed to determine the level of polyunsaturated

fatty acid (in percent). A sample of 6 packages resulted in the following data: 16.8, 17.2, 17.4,

16.9, 16.5, 17.1.Test the hypothesis Ho: µ=17 against H1: µ ≠ 17 using α=0.01.

Answer 1

Solution:

The parameter of interest is the true mean level of polyunsaturated fatty acid,$\mu$ .

$\mathrm{H}_0: \mu=17 \\ \mathrm{H}_1: \mu \neq 17 \\ \alpha=0.01 \\ t_{0}=\dfrac{\bar{x}-\mu_{0}}{\sqrt{n}}$

Reject $H_{0}$ if $t_{0}<-t_{\alpha / 2,n-1}$ where $-t_{0.005,5}=-4.032$ or $t_{0}>t_{0.005,5}=4.032$

$\bar{x}=16.98, \mathrm{~s}=0.318,\, \mathrm{n}=6 \\ \quad t_{0}=\dfrac{16.98-17}{0.318 / \sqrt{6}}=-0.154$

Since $-4.032<-0.154<4.032$ , do not reject the null hypothesis and conclude the true mean level is not significantly different from 17 % at $\alpha=0.01$ .