Question

QUESTION 2

1. A company that manufactures electronic components wants to evaluate the following hypothesis test, using a level of significance of 0.1.

   A random sample of 15 components was taken; 9 were tested at 80° F (X₁), and 6 were tested at 120° F (X₂). The results are given below

   S₁ =40,  S₂ =30

   If the null hypothesis is true, what is the distribution of the test statistic?

   		t distribution with 9 degree of freedom
   		t distribution with 11 degree of freedom
   		t distribution with 12 degree of freedom
   		t distribution with 10 degree of freedom

Answer 1

since the population variance are not same

so using excel

we have

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	9
Sample Mean	0
Sample Standard Deviation	40.0000
Population 2 Sample
Sample Size	6
Sample Mean	0
Sample Standard Deviation	30.0000
Intermediate Calculations			Calculations Area
Numerator of Degrees of Freedom	107438.2716		Pop. 1 Sample Variance	1600.0000
Denominator of Degrees of Freedom	8450.6173		Pop. 2 Sample Variance	900.0000
Total Degrees of Freedom	12.7137		Pop. 1 Sample Var./Sample Size	177.7778
Degrees of Freedom	12		Pop. 2 Sample Var./Sample Size	150.0000

option c is true

t distribution with 12 degree of freedom