Question

Assume that both populations are normally distributed. ​a) Test whether 2μ1≠μ2 at the α=0.05 level of significance for the given sample data.​ b) Construct a 95​% confidence interval about 2μ1−μ2.			Sample 1	Sample 2
		n	19	19
		x overbarx	11.7	14.4
		s	3.4	3.9

Answer 1

SOLUTION:

From given data,

Assume that both populations are normally distributed

	Sample 1	Sample 2
	= 19	= 19
	=11.7	= 14.4
	= 3.4	= 3.9

a) Test whether 2μ1≠μ2 at the α=0.05 level of significance for the given sample data

H₀ : 2μ₁ = μ₂ ( Null hypothesis )

H₁ : 2μ₁ ≠ μ₂ ( Alternative hypothesis )

- = 11.7 - 14.4 = -2.7

SE( - ) =

=

= 1.18699

Test statistic : t =  ( - ) / SE( - )

=  -2.7 / 1.18699

= - 2.2746

t = - 2.2746

degree of freedom =df = + - 2 = 19 + 19 -2 = 36

α=0.05 = > critical value = t_critical = 2.028

b) Construct a 95​% confidence interval about 2μ1−μ2

95% confidence interval is

( - ) t_critical * SE( - )

- 2.7   2.028 * 1.18699

- 2.7   2.407215

( - 2.7 - 2.407215 ) , ( - 2.7+ 2.407215 )

-5.1072 , -0.2927

confidence interval about 2μ1−μ2 is from -5.10 to -0.29