Two types of plastic are suitable for an electronics component manufacturer to use. the breaking strength of this plastic is important. it is known that σ1 =σ2 = 1.0 psi. from a random sample of size n1 =10 and n2 =12, you obtain ¯x1 =162.5 and ¯x2 = 155.0. the company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi (inclusive). (a) based on the sample information, should it use plastic 1? test this using α=0.05. write formal null and alternate hypotheses statements for the test. (b) find the p-value for this test.

(a) Null Hypothesis (H₀) = Mean of x₁ > Mean of x₂

Alternative Hypothesis (H₁) = Mean of x₁ ≠ Mean of x₂

(b) We will use here t-test for two sample means which is given by,

" alt="t = \frac{\bar_{x_{1}}-\bar_{x_{2}}}{\sqrt{s^2(\frac{1}{n_{1}}+\frac{1}{n_{2}} )}}" />" />

Putting all values we get, t = 17.5 with 20 degree of freedom

At α = 0.05

p-value = 95% Confidence Interval for the Difference ( 6.6068 , 8.3932 )

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.