Answer to Question #214094 in Statistics and Probability for Madimetja

Question

A melting point test of n=10 samples of a binder used in manufacturing a rocket propellant resulted in x =154:2°F. Assume that the melting point is normally distributed with Q=1:5°F: Suppose you want to test the claim that the temperature is different from 155°F: Test the hypothesis at a=0:05: Write down the hypothesis to be tested and show all the steps and calculations.

Answer 1

$H_0: \mu=155 \\ H_1: \mu ≠155 \\ α=0.05 \\ \bar{x}=154.2 \\ \sigma= 1.5 \\ n=10$

Test statistic:

$Z = \frac{\bar{x}- \mu}{\sigma / \sqrt{n}} \\ Z = \frac{154.2-155}{1.5/ \sqrt{10}}= -1.69 \\ Z_{α/2}=Z_{0.05/2} = 1.96$

Rejection criterion:

If $-Z_{α/2}≤Z≤Z_{α/2}$ then we should fail to reject H₀.

-1.69 > -1.96

$Z>Z_{α/2}$

Accept H₀.

The temperature is NOT different from 155°F