Question

ou are given the null and alternative hypotheses and the sample information shown below. Complete parts a and b below.

H0​: μ1−μ2=0 HA​: μ1−μ2≠0		Sample 1			Sample 2
		n1	equals=	130	n2	equals=	125
		s1	equals=	32	s2	equals=	37
		x overbarx1	equals=	150	x overbarx2	equals=	155

a. Develop the appropriate decision​ rule, assuming a significance level of

0.05

is to be used.

Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to two decimal places as​ needed.)

A.Reject

H0

if t< -1.96or t>1.96

B

Test the null hypothesis and indicate whether the sample information leads you to reject or fail to reject the null hypothesis. Use the test statistic approach.

Calculate the value of the test statistic.

Answer 1

Ho : μ1 − μ2 = 0
Ha : μ1 − μ2 ≠ 0

Level of Significance (l.o.s.) : = 0.05

Test Statistic :Two sample t test ( t test is used because population varinace is know )

Decision Criteria : Reject Ho at 5% l.o.s. if | t cal | > t tab,
where t tab = t(/2 , n1+n2-2) = t(0.025 , 253 ) = 1.969385.

Calculations : n1 = 130, n2 = 125, s1 = 32, s2 = 37, = 150 and   = 155

Also Sp = = 34.5411481

t cal = =   = -1.156546

Conclusion : Since | t cal | < t tab, we do not reject Ho at 5% l.o.s. thus conclude that there is no significant difference between the two population means i.e. μ1 − μ2 = 0.

Hope this answers your query!