Question

A company that manufactures electronic components wants to evaluate the following hypothesis test, using a level of significance of 0.1. Ho: M1-M2 = 0 Hii H1 - H2>0 A random sample of 15 components was taken: 9 were tested at 80' F (X1), and 6 were tested at 120° F (X2) Suppose the resulting test statistic is 1.25 and test statistic has t distribution with 13 degree of freedom. a) Find the P-value of the test. A company that manufactures electronic components wants to evaluate the following hypothesis test, using a level of significance of 0.1. HO: H1-H2 = 0 Hi: H1-H2>0 A random sample of 12 components was taken: 6 were tested at 80° F(X1). and 6 were tested at 120° F(X2) Xi = 832, X2 = 779, S1 =40, S2 =30 *The resulting test statistic hast distribution with 9 degree of freedom* b) Compute the lower bound of the confidence interval that is relevant to this problem.

Answer 1

Ans :

given that sample size n1 = 9

sample size n2 = 6

Test statistic :

t = 1.25

and it is given that test statistic has t distribution with 13 degrees of freedom

A company that manufacture electronic components wants to evaluate the following hypothesis test

To Test :

H0 :µ1- µ2 =0 versus H1 : µ1 - µ2 >0

this is right  tailed t - test for two difference between two population mean

the p - value of this test is :

given significance level = 0.1

p-value = P(t>1.25/H0)

p- value = 0.116667

a) Ans :

The p - value of the test is 0.116667

b)

To Test :

H0 :µ1- µ2 =0

H1 : µ1 - µ2 >0

given that

$\small \bar{X}$1 = 832 , $\small \bar{X}$ 2 = 779

n1=6

n2= 6

s1 = 40

s2 = 30

df = 9

The Lower bound of the confidence interval

1 1 (Ã1 – 2 – ta, n1 + n2 – 2 * Sp + n1 n2

(832 - 779 - (1.81)*20.41

(53 - (1.81 )*( 20.41) 0

(53 - 37)

16

The Lower bound of the confidence interval is 16